The following system of equations has to be solved using the elimination method:

2x - 4y = -24 ...(1)

7x + 3y = 1 ...(2)

To eliminate x determine 7*(1) - 2*(2)

7*(1) - 2*(2)

=> 14x - 28y - 14x - 6y = -168 - 2

=> -34y = -170

=> y = -170/-34

=> y = 5

To eliminate y determine 3*(1) + 4*(2)

3*(1) + 4*(2)

=> 6x - 12y + 28x + 12y = -72 + 4

=> 34x = -68

=> x = -68/34

=> x = -2

**The required solution using the elimination method is (-2, 5)**

2x-4y = -24..............(1)

7x +3y = 1..............(2)

First we will multiply (1) by 3 and multiply (2) by 4 then add.

==> 3*(1) ==> 6x -12y = -72

==> 4*(2) ==> 28x +12y = 4

Now we will add both equations:

==> 34x = -68

==> x = -68/34 = -2

==> x = -2

Now we will substitute x= -2 in equation (2) to find y.

==> 7x+3y = 1 ==> 7(-2) + 3y = 1

==> -14 + 3y = 1==> 3y = 15 ==> y= 5

**Then, the solution to the system is the pair (-2, 5)**