Question

Please help me

What is the y-value in the solution to this system of linear equations?

4x + 5y = −12

-2x + 3y = −16

A.) −4
B.)−2
C.)2
D.)5

Answer 1

To solve, use the substitution method.

4x + 5y = -12

Move the variable to the right and change sign.

4x = -12 - 5

Divide both sides of the equation by 4.

x = -3 - 5/4y

Substitute the given value of x into the lower equation.

-2 (-3 - 5/4y) + 3y = -16

Distribute -2 through the parenthesis.

6 + 5/2y + 3y = -16

Add like terms.

6 + 11/2y = -16

Use inverse operations to multiply both sides by 2.

12 + 11y = -32

Move the constant to the right side.

11y = -32 - 12

Solve.

11y = -44

Divide both sides by 11.

y = -4 (your answer)

Answer 2

`- 2x + 3y = - 16 \\ \\ 1. \: - 2x = - 3y - 16 \\ 2. \: ( - 2x)/( - 2) = ( - 3y - 16)/( - 2) \\ x = (3)/(2)y + 8 \\ or \\ 1. \: - 2x = - 16 - 3y \\ 2. \: x = - ( - 16 - 3y)/(2) \\ \\ c. \: 2`