Question

Use substitution to solve the following system of equations.

x + 4y = 8
2x - 5y = 29
I

Answer 1

`x = 8 - 4y \: \: eqn \: 1`

now in eqn 2

`2(8 - 4y) - 5y = 29`

`16 - 8y - 5y = 29`

`16 - 13y = 29`

`16 - 29 = 13y`

`13 = 13y`

`(13)/(13) = y`

`y = 1`

Now in eqn 1

`x = 8 - 4y`

`x = 8 - 4 * 1`

`x = 8 - 4`

`x = 4`

therefore x=4 & y=1 answer

Answer 2

(12, - 1 )

Explanation:

Given the 2 equations

x + 4y = 8 → (1)

2x - 5y = 29 → (2)

Rearrange (1), expressing x in terms of y by subtracting 4y from both sides

x = 8 - 4y → (3)

Substitute x = 8 - 4y into (2)

2(8 - 4y) - 5y = 29 ← distribute and simplify left side

16 - 8y - 5y = 29

16 - 13y = 29 ( subtract 16 from both sides )

- 13y = 13 ( divide both sides by - 13 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = 8 - 4(- 1) = 8 + 4 = 12

solution is (12, - 1 )