Answer:
[tex]B.\ -3x - 2y = 12[/tex]
[tex]C.\ 15x + 10y = -60[/tex]
[tex]E.\ 6x + 4y = -24[/tex]
[tex]F.\ 1.5x + y =-6[/tex]
Step-by-step explanation:
Given
[tex]3x + 2y = -12[/tex]
Required
Determine equations with same solution as [tex]3x + 2y = -12[/tex]
For a solution to have the same solution as [tex]3x + 2y = -12[/tex], the equation must be expressed as [tex]3x + 2y = -12[/tex]
[tex]A.\ 3x - 2y = 12[/tex]
This can not be expressed as [tex]3x + 2y = -12[/tex]
[tex]B.\ -3x - 2y = 12[/tex]
Multiply through by -1
[tex]-1(-3x - 2y) = 12 * -1[/tex]
[tex]3x + 2y = -12[/tex]
This has the same solution as the given equation
[tex]C.\ 15x + 10y = -60[/tex]
Divide through by 5
[tex]\frac{15x}{5} + \frac{10y}{5} = \frac{-60}{5}[/tex]
[tex]3x + 2y = -12[/tex]
This has the same solution as the given equation
[tex]D.\ 6x + 2y = -12[/tex]
Divide through by 2
[tex]\frac{6x}{2} + \frac{2y}{2} = \frac{-12}{2}[/tex]
[tex]3x + y = -6[/tex]
This can not be expressed as [tex]3x + 2y = -12[/tex]
[tex]E.\ 6x + 4y = -24[/tex]
Divide through by 2
[tex]\frac{6x}{2} + \frac{4y}{2} = \frac{-24}{2}[/tex]
[tex]3x + 2y = -12[/tex]
This has the same solution as the given equation
[tex]F.\ 1.5x + y =-6[/tex]
Multiply through by 2
[tex]2*1.5x + 2*y =-6*2[/tex]
[tex]3x + 2y =-12[/tex]
This has the same solution as the given equation
[tex]G.\ x + \frac{2}{3}y = -12[/tex]
Multiply through by 3
[tex]3 * x + 3*\frac{2}{3}y = -12*3[/tex]
[tex]3x + 2y = -36[/tex]
This can not be expressed as [tex]3x + 2y = -12[/tex]
The equations with the same solution as [tex]3x + 2y = -12[/tex] are the ones that we were able to expressed as [tex]3x + 2y = -12[/tex].
And the equations are:
[tex]B.\ -3x - 2y = 12[/tex]
[tex]C.\ 15x + 10y = -60[/tex]
[tex]E.\ 6x + 4y = -24[/tex]
[tex]F.\ 1.5x + y =-6[/tex]
