What is the solution of the system? also if you can, explain ? use the elimination method. −4x−2y=−12 2x+4y=−12

In order to find the solution (point of intersection) of two lines, you must solve them simultaneously for the x-coordinates and y-coordinates.

Let   -4x - 2y = -12    be (eq1)
 &     2x + 4y = -12    be  (eq2)

Now you have to find a way to multiply one or two of the equations so that upon adding or subtracting them, the two equations will become a single equation with one solvable variable.

     by multiplying (eq 1) by 2
                            2(-4x - 2y = -12)
             Now let     -8x - 4y = -24      (eq1ᵃ)

                          
        So,   -8x - 4y + (2x + 4y) = -24 + (-12)      [eq1ᵃ + eq2]
            ⇒   -8x + 2x - 4y + 4y = - 36 
                                       - 6x  = - 36
                                 ⇒       x  = 6

     By substituting x = 6 into  eq2
                ⇒ 2(6) + 4y = - 12
                       12 + 4y = - 12
                              4y = - 24
                            ⇒ y = -6

Thus the solution set is (6 , -6)