Question

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

Answer 1

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

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

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

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

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

`(15x)/(5) + (10y)/(5) = (-60)/(5)`

`3x + 2y = -12`

This has the same solution as the given equation

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

Divide through by 2

`(6x)/(2) + (2y)/(2) = (-12)/(2)`

`3x + y = -6`

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

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

Divide through by 2

`(6x)/(2) + (4y)/(2) = (-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 + (2)/(3)y = -12`

Multiply through by 3

`3 * x + 3*(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`