Solve the system of equations by the solution method?

Question

{4x-y=7
{7x-4y=10

what is the solution?

Answer 1

X = 2
Y = 1

Answer 2

4x - y = 7- - - - - - -Equation 1
7x - 4y = 10- - - - --Equation 2
- - - - - - - - -

Multiply equation 1 by - 4

4x - y = 7

- 4(4x) - (- 4)(y) = - 4(7)

- 16x - (- 4y) = - 28

- 16x + 4y = - 28

- - - - - - - - - - -

- 16x + 4y = - 28
7x - 4y = 10
- - - - - - - - - - - -
- 9x = - 18

- 9x / - 9 = - 18 / - 9

x = - 18 / - 9

x = 2

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - -

4x - y = 7

4(2) - y = 7

8 - y = 7

8 - y - 8 = 7 - 8

- y = - 1

- 1(- y) = - 1(- 1)

y = 1

Insert the y value into equation 1

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Check for equation 1

4x - y = 7

4(2) - 1 = 7

8 - 1 = 7

7 = 7

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Check for equation 2

7x - 4y = 10

7(2) - 4(1) = 10

14 - 4 = 10

10 = 10

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The solution set { 2, 1 }

- - - - - - - -s-

Answer 3

4x - y = 7
> 16x - 4y = 28 _ _ _ _(1)
7x - 4y = 10
> -7x + 4y = -10 _ _ _ _(2)

add (1) and (2)
9x = 18
> x = 18/9
> x = 2
substitute this in (1)
16(2) - 4y = 28
> 4y = 32 - 28
> y = 1

Answer 4

(4x-y=7)*4
7x-4y=10

9x=18
x=2,y=1