Question

Solve by substitution x+7y=0 2x-8y=22

Answer 1

`let \: \\ x + 7y = 0 \: \: \: - - - (a) \\ 2x - 8y = 22 \: \: \: - - - (b)`

`by \: substitution \: method....`
from eqn----(a)

`x + 7y = 0 \\ x = - 7y`
putting the value of x in eqn----(b)

`2x - 8y = 22 \\( 2 * - 7y) - 8y = 22 \\ - 14y - 8y = 22 \\ - 22y = 22 \\ y = - ( (22)/(22) )`

`y = - 1`
putting the value of y in eqn----(a)

`x + 7y = 0 \\ x + 7 * - 1 = 0 \\ x - 7 = 0 \\ x = 7`

Answer 2

(x, y) = (7, - 1)

Explanation:

given the 2 equations

x + 7y = 0 → (1)

2x - 8y = 22 → (2)

Rearrange (1) expressing x in terms of y by subtracting 7y from both sides

x = - 7y → (3)

Substitute x = - 7y in (2)

2(- 7y) - 8y = 22

- 14y - 8y = 22

- 22y = 22 ( divide both sides by - 22 )

y = - 1

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

x = - 7 × - 1 = 7

Solution is (7, - 1 )