Question

Use substitution to solve the following system of equations.
x + 4y = 8
2x - 5y = 29
I

Answer 1

Answer:

(12, - 1 )

Step-by-step 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 )

Answer 2

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

now in eqn 2

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

$16 - 8y - 5y = 29$

$16 - 13y = 29$

$16 - 29 = 13y$

$13 = 13y$

$\frac{13}{13} = y$

$y = 1$

Now in eqn 1

$x = 8 - 4y$

$x = 8 - 4 \times 1$

$x = 8 - 4$

$x = 4$

therefore x=4 & y=1 answer