Question

How many solutions are there to the following system of equations?
5x 3y=7
2x-y=2

Answer 1

5x + 3y = 7 (1)
2x - y = 2 (2)

Multiply (2) by 3:
6x - 3y = 6 (3)

Take (1) + (3):
(5x + 6x) + (3y-3y) = 7+6
⇒ 11x = 13
⇒ (11/11)*x= 13/11
⇒ x = 13/11.

y = 2*13/11 -2= 4/11

The final answer is x=13/11, y=4/11.