Question

Use the linear combination method to solve the system of equations. Please explain each step of your solution

Answer 1

Answer:

(2, -3)

Solve the equation

$\left \{ {{2x-3y=13} \atop {x+2y=-4}} \right.$

Rearrange like terms to the same side of the equation

$\left \{ {{2x-3y=13} \atop {x=-4-2y}} \right.$

Substitute into one of the equations

$2(-4-2y)-3y=13$

Apply the Distributive Property

$-8-4y-3y=13$

Combine like terms

$-8-7y=13$

Rearrange variables to the left side of the equation

$-7y=13+8$

Calculate the sum or difference

$-7y=21$

Divide both sides of the equation by the coefficient of variable

$y=-\frac{21}{7}$

Cross out the common factor

$y=-3$

Substitute into one of the equations

$x=-4-2\times(-3)$

Calculate

$x=2$

The solution of the system is

$\left \{ {{x=2} \atop {y=-3}} \right.$

I hope this helps you

:)