Solve by the elimination method?

Question

5x + 2y = -11
7x - 3y = 17

Answer 1

5x + 2y = -11
multiply the equation by 3
15x + 6y = -33 -------------> (a)
7x - 3y = 17
multiply the equation by 2
14x-6y=34 -------------> (b)
add equations (a) and (b)
15x + 6y = -33
14x - 6y = 34

29x = 1
divide each side by 39
x =1/29
substitute x =1/29 in 5x + 2y = -11
5 * 1/29 + 2y = -11
5/29 +2y = -11
subtract 5/29 from each side
5/29 +2y-5/29 = -11-5/29
2y = -324/29
y = -162/29
(x, y) = (1/29 , -162/29)