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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

Respuesta :

tmarsheuna

[tex] - 2x + 3y = - 16 \\ \\ 1. \: - 2x = - 3y - 16 \\ 2. \: \frac{ - 2x}{ - 2} = \frac{ - 3y - 16}{ - 2} \\ x = \frac{3}{2}y + 8 \\ or \\ 1. \: - 2x = - 16 - 3y \\ 2. \: x = - \frac{ - 16 - 3y}{2} \\ \\ c. \: 2[/tex]

Erin2626

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)

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