What is the solution the system of equations below? Show Work Please.... 10 Points

What is the solution the system of equations below?
x+2y=7a
3x-2y=5a

THANK YOU SO MUCH!! :-)

You need as many variables as equations to solve a system completely. You have two equations and three variables, so you can't find numbers for all the variables.
You can, however, solve for x and y in terms of a.

For this system the easiest first step is to add the equations together.
Remember that if A = B and C = D, then A + C = B + D.
(x + 2y) + (3x - 2y) = 7a + 5a
The y's add to 0, leaving 4x = 12a
x = 3a
Then replace x with 3a in either equation to solve for y.
y = 2a

Of course, you could treat a different variable as dependent and get a different type of solution:
x = 3/2 y
a = 1/2 y
or
y = 2/3 x
a = 1/3 x

Let first equation be (1) and 2nd equation be (2)

(1)+(2) => 4x=12a
x=3a

substituting x=3a into (1) we get
3a+2y=7a
2y=7a-3a
2y=4a
y=2a

therefore x=3a,y=2a