Hello!
[tex]\large\boxed{5, -8}[/tex]
5x + 2y = 9
4x - 3y = 44
We can eliminate y by multiplying both expressions in order to have the y coefficients equal.
The LCM (least common multiple) of 2 and 3 is 6, so we can multiply each accordingly:
3(5x + 2y = 9)
2(4x - 3y = 44)
Distribute:
15x + 6y = 27
8x - 6y = 88
Cancel using addition:
15x + 6y = 27
8x - 6y = 88
------------------
23x = 115
Divide:
x = 5.
Plug in this value of x into an equation to solve for y:
5(5) + 2y = 9
25 + 2y = 9
2y = -16
y = -8
The solution of the system is:
(5, -8).
