1. Multiply the second equation by 5 to get rid of the -2y term:
40x - 10y = -10
2. Add this new equation to the first equation:
(9x + 5y) + (40x - 10y) = 34 + (-10)
49x = 24
3. Solve for x:
x = 24/49
4. Substitute x = 24/49 into one of the original equations (let's use the first one) and solve for y:
9(24/49) + 5y = 34
5y = 34 - (216/49)
5y = (166/49)
y = (166/49) * (1/5)
y = 166/245
5. Check the solution by plugging both x and y back into the original equations:
9(24/49) + 5(166/245) = 34
8(24/49) - 2(166/245) = -2
Both equations are true, so the solution is (24/49, 166/245).