Question

Which of the following equations has the same solutions as the equation 3x + 2y = -12? Check all that apply.

Answer 1

Answer:

$B.\ -3x - 2y = 12$

$C.\ 15x + 10y = -60$

$E.\ 6x + 4y = -24$

$F.\ 1.5x + y =-6$

Step-by-step explanation:

Given

$3x + 2y = -12$

Required

Determine equations with same solution as $3x + 2y = -12$

For a solution to have the same solution as $3x + 2y = -12$, the equation must be expressed as $3x + 2y = -12$

$A.\ 3x - 2y = 12$

This can not be expressed as $3x + 2y = -12$

$B.\ -3x - 2y = 12$

Multiply through by -1

$-1(-3x - 2y) = 12 * -1$

$3x + 2y = -12$

This has the same solution as the given equation

$C.\ 15x + 10y = -60$

Divide through by 5

$\frac{15x}{5} + \frac{10y}{5} = \frac{-60}{5}$

$3x + 2y = -12$

This has the same solution as the given equation

$D.\ 6x + 2y = -12$

Divide through by 2

$\frac{6x}{2} + \frac{2y}{2} = \frac{-12}{2}$

$3x + y = -6$

This can not be expressed as $3x + 2y = -12$

$E.\ 6x + 4y = -24$

Divide through by 2

$\frac{6x}{2} + \frac{4y}{2} = \frac{-24}{2}$

$3x + 2y = -12$

This has the same solution as the given equation

$F.\ 1.5x + y =-6$

Multiply through by 2

$2*1.5x + 2*y =-6*2$

$3x + 2y =-12$

This has the same solution as the given equation

$G.\ x + \frac{2}{3}y = -12$

Multiply through by 3

$3 * x + 3*\frac{2}{3}y = -12*3$

$3x + 2y = -36$

This can not be expressed as $3x + 2y = -12$

The equations with the same solution as $3x + 2y = -12$ are the ones that we were able to expressed as $3x + 2y = -12$.

And the equations are:

$B.\ -3x - 2y = 12$

$C.\ 15x + 10y = -60$

$E.\ 6x + 4y = -24$

$F.\ 1.5x + y =-6$