See graph

y = 2x - 6 is a straight line through (0,-6) and (3,0).

x - 2y = -3 is a straight line through (0,3/2) and (-3,0).

The intersection will be at (5,4).

(x,y) = (5,4) is the solution

https://gyazo.com/1f7d097d6e55552eee4be6aae2c982b6