Answer:
Option A.
Step-by-step explanation:
step 1
Find the solution of the system of linear equations given
we have
[tex]6x+2y=-6[/tex] -----> equation A
[tex]3x-4y=-18[/tex] -----> equation B
Solve the system of equation by graphing
The solution of the system of equations is the intersection point both graphs
The intersection point is (-2,3)
see the attached figure
step 2
Find the equivalent system of equations that will produce the same solution as the one given
Observing the linear equations
The value of x of case A is x=-2 and the value of y case D is y=3
Verify case A and case D
Substitute the value of x and the value of y in each equation and then compare the results
case A)
First equation
[tex]12(-2)+4(3)=-12[/tex]
[tex]-24+12=-12[/tex]
[tex]-12=-12[/tex] ------> is true
Second equation
[tex]15(-2)=-30[/tex]
[tex]-30=-30[/tex] ----> is true
therefore
The case A) is an equivalent system that will produce the same solution as the one given
case D)
First equation
[tex]6(-2)+(3)=15[/tex]
[tex]-12+3=-12[/tex]
[tex]--9=-12[/tex] -----> is not true
therefore
The case D) is not an equivalent system that will produce the same solution as the one given
