I'm not certain what you are asking here, but you've posted two linear equations in x and y. They are not the SAME equation, so they have a single shared solution in X and Y.
The easiest approach to finding this solution (with or without a calculator) is to solve each of them for "Y". Then you can either set them equal to each other and solve for X, or you can graph them both and see where they cross.
solvle 1st equation for y: 5x - 4y = -3
5x - 5x - 4y = -3 - 5x ; subtract 5x from both sides
-4y = -5x - 3 ;
-4y/-4 = (-5x - 3) / 4 ; divide both sides by -4
y = (5/4)x + 3/4
Solve 2nd equation for y: x - 2y = -15
x - x - 2y = -15 - x ; subtract -x from both sides
-2y = -x - 15
(-2y)/-2 = (-x - 15)/-2 ; divide both sides by -2
y = x/2 + 15/2
Since you solved them both for y, you can set the two "x" expressions equal to each other and solve for x.
(5/4)x + 3/4 = x/2 + 15/2 ; multiply everything by 4
5x + 3 = 2x + 30 ; subtract 2x from both sides
3x + 3 = 30 ; subtract 3 from both sides
3x = 27 ; divide both sides by 3
x = 9
Now substitute the 9 for x in either original equation and solve for y.
y = 9/2 + 15/2
y = 24/2
y = 12
So, the final answer is (9, 12).
