Find the solution of this system of equations 3x+2y= -21 -7x-4y=33

The system is 

 i) 3x+2y=-21
ii) -7x-4y=33.

We notice that we can eliminate the y's by multiplying the first equation by 2, and adding this equation to the second one, as follows:

multiplying equation (i) by 2 we have

 i) 6x+4y=-42
ii) -7x-4y=33.

Adding these equations side by side, we get:

            6x-7x=-42+33, which simplifies to -x=-9, thus x=9.

Since 3x+2y=-21, substituting x=9, we can find y:

                                3(9)+2y=-21
                                   27+2y=-21
                                          2y=-21-27
                                            2y=-48
                       thus y=-28/2=-24.

The solution of the system is (x,y)=(9, -24). 

The first equation given is:
3x + 2y = -21
This can be rewritten as:
2y = -21 - 3x > equation I

The second given equation is:
-7x - 4y = 33
This can be rewritten as:
-7x - 2(2y) = 33 > equation II

Substitute with equation I in equation II to get the value of x as follows:
-7x - 2(2y) = 33
-7x -2(-21-3x) = 33
-7x + 42 + 6x = 33
-x = 33-42 = -9
x = 9

Substitute with the value of x in equation I to get the value of y as follows:
2y = -21 - 3x 
2y = -21 -3(9)
2y = -21-27 = -48
y = -24

Based on the above calculations:
x - 9
y = -24