Question

Use the substitution method to solve this system of equations. Choose the correct ordered pair. 2x-y=10. 2x-2y=4

Answer 1

(x, y) = (8, 6)

Explanation:

given the 2 equations

2x - y = 10 → (1)

2x - 2y = 4 → (2)

rearrange equation (1) expressing y in terms of x

y = 2x - 10 → (3)

Substitute y = 2x - 10 in equation (2)

2x - 2(2x - 10) = 4

2x - 4x + 20 = 4

- 2x + 20 = 4 ( subtract 20 from both sides )

- 2x = - 16 ( divide both sides by - 2 )

x = 8

substitute x = 8 in equation (3)

y = (2 × 8) - 10 = 16 - 10 = 6

solution is (8 , 6)

Answer 2

ANSWER

The correct ordered pair is

`(8,6).`



EXPLANATION

The given equations are

`2x - y = 10`


We make y the subject and call it equation (1).


Thus,


`- y = - 2x + 10`


This implies that,



`y = 2x - 10 - - - (1)`


The second equation is


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


We substitute equation (1) into equation (2).


`2x - 2(2x - 10) = 4`


We expand brackets to obtain,


`2x - 4x + 20 = 4`


This implies that,


`2x - 4x= 4 - 20`



`- 2x = - 16`


`x = 8`


We put this value in to equation (1) to get,


`y = 2(8) - 10`


`y = 16 - 10`



`y = 6`


The correct orders pair is

`(8,6)`