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

Which Of The Following Equations Has The Same Solutions As The Equation 3x 2y 12 Check All That Apply class=

Sagot :

MrRoyal

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]

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