you can use elimination by adding the two equations to "cancel out" one of the variables. in this example y will cancel out.
2x + y = 3
+
2x - y = 4
________
2x = 6
x = 3
now that we know our x value, we can plug it into one of the other equations to get our y value.
2(3) + y = 3
6 + y = 3
y = -3
your answer for this system is x=3, y=-3