Solve with elimination method?

Question

4x + y = 9
3x - 2y = 4


4x - 3y = -4
3x - 2y = -4

Thank you

Answer 1

4x + y = 9- - - -Equation 1
3x - 2y = 4- - - - Equation 2
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Multiply equation 1 by 2

4x + y = 9

2(4x) + 2(y) = 2(9)

8x + 2y = 18. . .new equation 1

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Elimination of y

8x + 2y = 18
3x - 2y = 4
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11x = 22

11x / 11 = 22 / 11

x = 22/11

x = 2

The answer is x = 2

Insert the x value into equation 1

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4x + y = 9

4(2) + y = 9

8 + y = 9

8 + y - 8 = 9 - 8

y = 1

The answer is y = 1

Insert the y value into equation 1

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Check for equation 1

4x + y = 9

4(2) + 1 = 9

8 + 1 = 9

9 + 9

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Check for equation 2

3x - 2y = 4

3(2) - 2(1) = 4

6 - 2 = 4

4 = 4

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The solution set { 2, 1 }

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Problem 2

4x - 3y = - 4- - - - -Equation 1
3x - 2y = - 4- - - - -Equation 2
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Multiply equation 1 by - 2 and equatiion 2 by 3

4x - 3y = - 4

-2(4x) - ( - 2)(3Y) = - 2(- 4)

- 8x - (- 6y) = - (-8

- 8 + 6y = 8. . . .New equation 1

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3x - 2y = - 4

3(3x) - 3(2y) = 3(- 4)

9x - 6y = - 12. . .New equation 2

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- 8x + 6y = 8
9x - 6y = - 12
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x = - 4

The answer is x = - 4

Insert the x value into equation 1

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4x - 3y = - 4

4(- 4) - 3y = - 4

- 16 - 3y = - 4

- 16 - 3y + 16 = - 4 + 16

- 3y = 12

- 3y / - 3 - 12 / - 3

y = - 4

The answer is y = - 4

Insert the y value into equatio 1

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Check for equation 1

4x - 3y = - 4

4( - 4) - 3( -4) = - 4

- 16 - (- 12) = - 4

- 16 + 12 = - 4

- 4 = - 4

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Check for equatiion 2

3x - 2y = - 4

4(- 4) - 2( - 4) = - 4

- 16 - (- 8) = - 4

- 16 + 8 = - 4

- 4 = - 4

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The solution set is { -4, - 4 }

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Answer 2

4x + y = 9 to set up Elimination method 8x + 2y = 18
3x - 2y = 4 Find a common factor 3x - 2y = 4
Just subtract and Common cancels out 5x = 14
x = 5/14 or 0.357142857
then put 5/14 in place of x with the top or bottom original equation.

so 4(5/14) + y = 9
4/1 * 5/14 = 10/7
10/7 + y = 9
subtract 10/7 from both sides so
y = 53/7 or 7.57142857
so x = 5/14 or 0.357142857
and y = 53/7 or 7.57142857

Answer 3

When solving by elimination, you want to get either the x's or the y's to have opposite coefficients. For example in your first problem, you can easily make the y's opposite by multiplying the first equation by 2.

(4x + y = 9) times 2
3x - 2y = 4

turns into

8x +2y = 18
3x - 2y = 4

Now if you add both equations together...you get

11x = 22.

Solve for x here to get x = 2. Then substitute 2 in for x in either of the original equations and solve for y...

The second problems are similar, but you need to mulitply both equations in order to get opposite coefficients..

Answer 4

Here is one method for the first one,

4x + y = 9 (1)
3x - 2y = 4 (2)

Rewrite (1) as, y=9-4x, then substitute into (2),
3x-2(9-4x) = 4, which gives,

3x-18+8x = 4, which gives,

11x=22, i.e. x=2, then substitute into (1),

4(2)+y=9, so y=1. your solution is, x=2, y=1

Answer 5

a)
7x-y=13
x=(13+y)/7
4{(13/7+y/7)} +y =9
13/7+y/7=9/4
y=(9/4-13/7)7=63/4-13
y=15 3/4-13
y=2 3/4=2.75
x=(9-2 3/4)/4= 6.25 /4=25/16= 1.56

b)
7x-5y= -8
x= (-8 +5y)/7
4{(-8+5y)/7}-3y = -4
(-32+20y)/7 -3y= -4
-32/7 +20y/7 -3y= -4
20/7 (y)-3y = -4 -32/7
y(20/7 -3)= -60/7
y= -60/7 +1/7= -59/7= -8.43
x= {-4+3(-59/7)}/4= -1 + 3/4(-59/7)= -1.632

ooops sorry that was the addition method....must have messed up somewhere??? Ow...