# 2x+y+3z=1,2x+6y+8z=3,6x+8y+18z=52x+y+3z=1,2x+6y+8z=3,6x+8y+18z=5

**WALDEN**

**What lesson does Thoreau use in describing the bug in the wood?**

In Walden, Thoreau uses the image of an egg becoming a bug emerging from a 60-year-old table to show how change can occur, and that one’s true self can be resurrected and become renewed. Like…

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**CRISPIN: THE CROSS OF LEAD**

**Write based on the reading, what was everyday life like in the 14th century England for the serfs…**

The story opens with Crispin recounting the events of his mother’s burial. Our young protagonist is only thirteen, but for a boy living in 14th century England, he soon finds his life becoming more…

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**RAYMOND’S RUN**

**What conclusions can you draw about Sqeaky from her description of Gretchen in “Raymond’s Run”?…**

Squeaky dismisses Gretchen because she thinks she is a phony, and this shows how important effort and authenticity is to Squeaky. To Squeaky, Gretchen is inferior because she is all talk. While…

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**HISTORY**

**Why was the Supreme Court against FDR’s New Deal?**

The relationship between Franklin D. Roosevelt and the courts was tenuous at best. One can imagine the frustration of the president with the popular success of his social reform programs being in…

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**CRISPIN: THE CROSS OF LEAD**

**What was everyday life like in 14th century England for the serfs and for the nobility?**

Crispin: The Cross of Lead is a 2002 children’s novel written by the American writer Edward Irving Wortis under the pseodonym “Avi.” The story begins in 1377 A.D. The protagonist is a 13-year-old…

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**HISTORY**

**What techniques did the Nazis use to appeal to the public?**

The use of propaganda and silencing dissent were two techniques that the Nazis used to appeal to the public. “Propaganda” is biased or skewed information intended to advance a particular political…

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**THE GIVER**

**Name three steps of the escape plan in The Giver**

We learn about the escape in Ch. 20. It took quite a bit of preparation, including steps that they plan to take both before and after Jonas leaves the community. Here are the first three steps to…

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**HISTORY**

**What appeals did the Nazis use? What are some examples?**

After World War I, the country of Germany was in a crisis. People were disoriented and looking for answers. As a result, the Nazis were able to use several appeals to encourage people to support…

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**MY SIDE OF THE MOUNTAIN**

**What was the biggest problem Sam faced with this task?**

Sam Gribley was a city kid who ran away from home to go to live on the wild property of his ancestors in the Catskill Mountains. He took only a penknife, a ball of cord, an ax, and $40. With these…

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**THE PRINCE AND THE PAUPER**

**Why did the thieves and beggars drink to the English law?**

In Chapter 17, Prince Edward has been lured into John Canty’s clutches again. We are told in this chapter that Canty now calls himself John Hobbs. Meanwhile, the death of King Henry VIII, Edward’s…

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**HISTORY**

**How did the American economy come to be dominated by monopolistic corporations in industries such…**

The main reason the American economy came to be dominated by monopolistic corporations in the post-Civil War era was that these businesses functioned in an essentially regulation-free environment….

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**A WORN PATH**

**What is the meaning of the short story “A Worn Path” by Eudora Welty?**

Eudora Welty’s “A Worn Path” touches on a few different themes. The story shows the strength of love and perseverance. The trip she makes along the worn path to Natchez to get medicine for…

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**THE WATSONS GO TO BIRMINGHAM—1963**

**In The Watsons Go to Birmingham—1963, what kind of dog is Toddy?**

In The Watsons Go to Birmingham—1963, Mr. Robert calls his dog, Toddy, a “coon dog.” Toddy is a type of dog called a coonhound. Coonhounds were specifically bred in America to be hunting…

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**MACBETH**

**What is Act IV, Scene 1 in Macbeth about?**

This scene is highly significant to the course of the play. In Act IV, Scene 1, Macbeth visits the witches again, seeking answers to pressing questions about his rise to power and his future. The…

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**HISTORY**

**What was the effect of Greek colonization in the Mediterranean?**

The most practical benefit or effect of Greek colonies throughout the Mediterranean Sea was the supply of food and other material to the city-states of the Greek mainland. Mainland Greece is not…

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**SCIENCE**

Plate tectonics refers to the idea of Earth’s outer layer being divided into a number of fragments or plates, all of which are in constant motion. These fragments or plates are known as tectonic…

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**THE MONK**

**I need to find a short summary of the novel The Monk by Matthew Gregory Lewis.**

The Monk by Matthew Gregory Lewis was published in 1796 and is considered one of the classic exemplars of the late eighteenth-century Gothic Romance. It is set in Madrid, Spain, and has a complex…

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**HENRY**

**“The Cop and the Anthem” by O. Henry What is your opinon of the short story? How was it? Please…**

“The Cop and the Anthem” is both funny and serious. Like O. Henry’s story “A Retrieved Reformation,” it deals with the subject of reformation and the difficulties people face in trying to reform….

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**JOHNNY TREMAIN**

**What ideas would be most worthy of a literary discussion about Johnny Tremain?**

Interesting question! In the book Johnny Tremain by Esther Forbes, there are numerous components worthy of literary discussion. However, some of the more interesting components include the book’s…

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**TO KILL A MOCKINGBIRD**

**What is the final outcome in the novel To Kill a Mockingbird?**

The outcome of the novel To Kill a Mockingbird involves Atticus losing the Tom Robinson case, the death of the Bob Ewell, Boo Radley’s heroic efforts to save the children, Scout’s understanding of…

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**FLOWERS FOR ALGERNON**

**How does Miss Kinnian react when Charlie returns to night school?**

In the story, Flowers for Algernon, Charlie is the main character and Miss Kinnian is his teacher. At first, Charlie does not understand much of school but tries hard. Miss Kinnian recommends him…

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**MATH**

**x+y+z+w=6,2x+3y−w=0,−3x+4y+z+2w,=4,x+2y−z+w=0x+y+z+w=6,2x+3y-w=0,-3x+4y+z+2w,=4,x+2y-z+w=0Solve the…**

You may use the reduction method to solve the system, hence, you may multiply the first equation by 3, such that: 3(x+y+z+w)=3⋅63(x+y+z+w)=3⋅6 3x+3y+3z+3w=183x+3y+3z+3w=18 You may now add the equation…

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**MATH**

**x+3w=4,2y−z−w=0,3y−2w=1,2x−y+4z=5x+3w=4,2y-z-w=0,3y-2w=1,2x-y+4z=5Solve the system of linear…**

3w+x=43w+x=4 (equation 1) −w+2y−z=0-w+2y-z=0 (equation 2) 3y−2w=13y-2w=1 (equation 3) 2x−y+4z=52x-y+4z=5 (equation 4) Add 1/3 × (equation 1) to equation 2:3w+x+0y+0z=43w+x+0y+0z=4…

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**MATH**

**2x+3y+3z=7,4x+18y+15z=442x+3y+3z=7,4x+18y+15z=44 Solve the system of linear equations and check any…**

You should notice that the system is indeterminate, since the number of variables is larger than the number of equations. 2⋅(2x+3y+3z)=14⇒4x+6y+6z=14⇒4x=14−6y−6z2⋅(2x+3y+3z)=14⇒4x+6y+6z=14⇒4x=14-6y-6z…

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**MATH**

**2x−3y=−2,−4x+9y=72x-3y=-2,-4x+9y=7 Solve the system of linear equations and check any solutions…**

You may use the reduction method to solve the system, hence, you may multiply the first equation by 2, such that: 2(2x−3y)=2⋅(−2)2(2x-3y)=2⋅(-2) 4x−6y=−44x-6y=-4 You may now add the equation 4x−6y=−44x-6y=-4…

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**MATH**

You may add the third equation to the first, such that: 4y−16z=−4⇒y−4z=−14y-16z=-4⇒y-4z=-1 You may add the second equation to the third, multiplied by 2, such that:

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**MATH**

**x+2y−7z=−4,2x+y+z=13,3x+9y−36z=−33x+2y-7z=-4,2x+y+z=13,3x+9y-36z=-33Solve the system of linear…**

You need to multiply the first equation by -2: −2x−4y+14z=8-2x-4y+14z=8You need to add this equation to the second: −3y+15z=21⇒−y+5z=7-3y+15z=21⇒-y+5z=7 You need to multiply the first equation by -3:…

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**MATH**

**x−3y+2z=18,5x−13y+12z=80x-3y+2z=18,5x-13y+12z=80 Solve the system of linear equations and check any…**

You should notice that the system has a smaller number of equations than the number of variables, hence, the system is indeterminate. x=3y−2z+18x=3y-2z+18 Replace 3y−2z+183y-2z+18 for x in the second…

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**MATH**

**x−2y+5z=2,4x−z=0x-2y+5z=2,4x-z=0 Solve the system of linear equations and check any solutions…**

Since the number of equations is smaller than the numbers of variables, the system is indeterminate. You may write the first equation, such that: x+5z=2+2yx+5z=2+2y You need to use a greek letter…

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**MATH**

**x+2z=5,3x−y−z=1,6x−y+5z=16x+2z=5,3x-y-z=1,6x-y+5z=16 Solve the system of linear equations and…**

You may replace 5−2z5-2z for x in the second and third equations, such that: 3(5−2z)−y−z=1⇒−y−7z=−143(5-2z)-y-z=1⇒-y-7z=-14 6(5−2z)−y+5z=16⇒−y−7z=−146(5-2z)-y+5z=16⇒-y-7z=-14 You should notice that you have…

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**MATH**

**3x−3y+6z=6,x+2y−z=5,5x−8y+13z=73x-3y+6z=6,x+2y-z=5,5x-8y+13z=7 Solve the system of linear equations…**

First, divide the first equation by 3 and obtain x-y+2z=2. Then express x=y-2z+2 and substitute it into the second and third equations: y-2z+2+2y-z=5, or 3y-3z=3, or y-z=1, and 5y-10z+10-8y+13z=7,…

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**MATH**

(1) 2x−2y−6z=−42x-2y-6z=-4 (2) −3x+2y+6z=1-3x+2y+6z=1 (3) x−y−5z=−3x-y-5z=-3 Use equations (1) and (2) to eliminate the y and z variables. (1) 2x−2y−6z=−42x-2y-6z=-4 (2) −3x+2y+6z=1-3x+2y+6z=1___________________ −x=−3-x=-3…

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**MATH**

**x+4z=1,x+y+10z=10,2x−y+2z=−5x+4z=1,x+y+10z=10,2x-y+2z=-5 Solve the system of linear equations and…**

Eq 1 : x+4z=1x+4z=1 Eq 2 : x+y+10z=10x+y+10z=10 Eq 3 :2x−y+2z=−52x-y+2z=-5 Multiply equation 1 by -1, −1(x+4z)=−1-1(x+4z)=-1 −x−4z=−1-x-4z=-1 Now add the above equation and equation 2, (−x−4z)+(x+y+10z)=−1+10(-x-4z)+(x+y+10z)=-1+10 Eq 4:y+6z=9y+6z=9…

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**MATH**

**4x+3y+17z=0,5x+4y+22z=0,4x+2y+19z=04x+3y+17z=0,5x+4y+22z=0,4x+2y+19z=0Solve the system of linear…**

You may subtract the third equation from the first, such that: y−2z=0⇒y=2zy-2z=0⇒y=2z Replace 2z for y in equations 2 and 3, such that:

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**MATH**

**2x+3y=0,4x+3y−z=0,8x+3y+3z=02x+3y=0,4x+3y-z=0,8x+3y+3z=0 Solve the system of linear equations and…**

Eq1: 2x+3y=02x+3y=0 Eq2:4x+3y−z=04x+3y-z=0 Eq3:8x+3y+3z=08x+3y+3z=0Multiply equation 2 by 3, 12x+9y−3z=012x+9y-3z=0 Now add the above equation and equation 3, (8x+3y+3z)+(12x+9y−3z)=0(8x+3y+3z)+(12x+9y-3z)=0 8x+12x+3y+9y+3z−3z=08x+12x+3y+9y+3z-3z=0 20x+12y=020x+12y=0…

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**MATH**

You may use reduction method, hence, you may subtract the first equation from the second, such that: 5y+5z=25y+5z=2 You may multiply the first equation by -3 and then you may add it to the third:…

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**MATH**

**3x−5y+5z=1,5x−2y+3z=0,7x−y+3z=03x-5y+5z=1,5x-2y+3z=0,7x-y+3z=0 Solve the system of linear equations…**

EQ1: 3x−5y+5z=13x-5y+5z=1 EQ2: 5x−2y+3z=05x-2y+3z=0 EQ3: 7x−y+3z=07x-y+3z=0 To solve this system of equations, let’s use elimination method. In elimination method, a variable or variables should be eliminated to get…

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**MATH**

**5x−3y+2z=3,2x+4y−z=2,x+y−z=−15x-3y+2z=3,2x+4y-z=2,x+y-z=-1 Solve the system of linear equations and…**

Eq. 1 : 5x−3y+2z=35x-3y+2z=3 Eq. 2 : 2x+4y−z=22x+4y-z=2 Eq. 3 : x+y−z=−1x+y-z=-1 Multiply Eq. 2 by 2 and add Eq. 1, 4x+8y−2z=44x+8y-2z=4 5x−3y+2z=35x-3y+2z=3 Eq.4 : 9x+5y=79x+5y=7 Subtract Eq. 3 from Eq. 2, Eq.5 : x+3y=3x+3y=3 Now let’s solve…

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**MATH**

**2x+y−z=7,x−2y+2z=−9,3x−y+z=52x+y-z=7,x-2y+2z=-9,3x-y+z=5 Solve the system of linear equations and…**

You may use the reduction method to solve the system, hence, you may multiply the first equation by 2, such that: 2(2x+y−z)=2⋅2(2x+y-z)=2⋅ 7 4x+2y−2z=144x+2y-2z=14 You may now add the equation

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**MATH**

**2x+4y+z=1,x−2y−3z=2,x+y−z=−12x+4y+z=1,x-2y-3z=2,x+y-z=-1 Solve the system of linear equations and…**

From the third equation z=x+y+1.z=x+y+1. Substitute it into the first two equations and obtain 2x+4y+x+y+1=1,2x+4y+x+y+1=1, or 3x+5y=0,3x+5y=0,and x−2y−3x−3y−3=2,x-2y-3x-3y-3=2, or 2x+5y=−5.2x+5y=-5. Now subtract these two equations to…

1 educator answer

**MATH**

**2x+2z=2,5x+3y=4,3y−4z=42x+2z=2,5x+3y=4,3y-4z=4 Solve the system of linear equations and check any…**

You may use the substitution method to solve the system, hence, you need to use the first equation to write x in terms of z, such that: 2x+2z=2⇒x+z=1⇒x=1−z2x+2z=2⇒x+z=1⇒x=1-z You may now…

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**MATH**

**x+y+z=5,x−2y+4z=13,3y+4z=13x+y+z=5,x-2y+4z=13,3y+4z=13 Solve the system of linear equations and…**

You may use the substitution method to solve the system, hence, you need to use the first equation to write x in terms of y and z, such that: x+y+z=5⇒x=5−y−zx+y+z=5⇒x=5-y-z You may now replace…

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**MATH**

**x+y+z=7,2x−y+z=9,3x−z=10x+y+z=7,2x-y+z=9,3x-z=10 Solve the system of linear equations and check…**

Add the third equation to the first and the second to eliminate z: 4x+y=17, 5x-y=19. Now add these equation to eliminate y: 9x=36, so x=4. Then y=17-4x=1 and z=3x-10=2. Check the answer:…

1 educator answer

**MATH**

**(15)x+(12)y=−13,x+y=−35(15)x+(12)y=-13,x+y=-35 Solve the system of linear equations and check any…**

(15)x+(12)y=−13(15)x+(12)y=-13 x+y=−35x+y=-35 Multiply first equation by 2, 2×5+y=−262×5+y=-26 Subtract the above equation from the second equation, (x−2×5)=−35−(−26)(x-2×5)=-35-(-26) 5x−2×5=−35+265x-2×5=-35+26 3×5=−93×5=-9…

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**MATH**

Multiply the second equation by 5 and add it to the first one to eliminate x:x: 0.8y+y=−0.1−3.5,0.8y+y=-0.1-3.5, or 1.8y=−3.6.1.8y=-3.6. So y=−3.61.8=−2y=-3.61.8=-2 and x=−0.1+0.8y1.5=1.x=-0.1+0.8y1.5=1. The answer: x=1x=1 and y=−2.y=-2….

1 educator answer

**MATH**

**x+2y=1,5x−4y=−23x+2y=1,5x-4y=-23 Solve the system of linear equations and check any solutions…**

EQ1: x+2y=1x+2y=1 EQ2: 5x−4y=−235x-4y=-23 To solve this system of equation, let’s apply substitution method. So let’s isolate the x in the first equation. x+2y=1x+2y=1 x=1−2yx=1-2y Then, plug-in this to…

1 educator answer

**MATH**

**3x−y=9,x−2y=−23x-y=9,x-2y=-2 Solve the system of linear equations and check any solutions…**

3x−y=93x-y=9 x−2y=−2x-2y=-2 From the second equation, x=−2+2yx=-2+2y Substitute the above expression of x in the first equation, 3(−2+2y)−y=93(-2+2y)-y=9 −6+6y−y=9-6+6y-y=9 −6+5y=9-6+5y=9 5y=9+65y=9+6 5y=155y=15 y=155y=155 y=3y=3 Plug the…

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**MATH**

**2x−y=0,x−y=72x-y=0,x-y=7 Solve the system of linear equations and check any solutions…**

EQ1: 2x-y=0 EQ2: x-y=7 To solve this system of equations, let’s apply substitution method. Let’s isolate the x in the second equation. x−y=7x-y=7 x=7+yx=7+y Then, plug-in this to the first equation….

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**MATH**

**−2x+3y=10,x+y=0-2x+3y=10,x+y=0 Solve the system of linear equations and check any solutions…**

−2x+3y=10-2x+3y=10 x+y=0x+y=0 Now let’s solve the equations by substitution method, From second equation, x=−yx=-y Substitute the above expression of x in the first equation, −2(−y)+3y=10-2(-y)+3y=10 2y+3y=102y+3y=10 5y=105y=10…

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**MATH**

**5x−8z=22,3y−5z=10,z=−45x-8z=22,3y-5z=10,z=-4 Use back substitution to solve the system of equations.**

EQ1: 5x−8z=225x-8z=22 EQ2: 3y−5z=103y-5z=10 EQ3: z=−4z=-4 In this system of equations, the value of variable z is given. So to get the values of the other variables plug-in z=-4. Plugging z=-4 to the first…

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