Verified answer

Eqn1: 4x + 3y = a

Eqn2: 3x + 2y = b

2•Eqn1 - 3•Eqn2:

-x = 2a - 3b

x = 3b - 2a

3•Eqn1 - 4•Eqn2:

y = 3a - 4b

(x,y) = (3b - 2a,3a - 4b)

You can only solve in terms of a and b. Let's use elimination to eliminate the x and solve that way:

3 * (4x + 3y) = 3 * a

12x + 9y = 3a

4 * (3x + 2y) = 4 * b

12x + 8y = 4b

12x + 9y = 3a

12x + 8y = 4b

____________

0x + 1y = 3a - 4b

So y = 3a - 4b.

Plug that back into either of the original equations to solve for x. Let's use the first:

4x + 3y = a

4x + 3(3a - 4b) = a

4x + 9a - 12b = a

4x + 9a = a + 12b

4x = -8a + 12b

x = -2a + 3b

or

x = 3b - 2a

That's as far as you can go. Done!

Solve either equation for x or y. In this case, I used the first one.

3y =a -3x

y = a/3 – x

3x +2(a/3-x) = b

3x +2a/3 -2x =b

X + 2/3 a =b

X = b – 2/3 a

Now, you can plug in x into an equation to solve for y.