Step 1 :Rewrite both equations in slope-intercept form (y = mx + b):
Step 2 :\(y = \frac{2}{5}x - 2\)
Step 3 :\(y = 6 - \frac{6}{5}x\)
Step 4 :Find the point of intersection, which is the solution to the system:
Step 5 :\(x = 5, y = 0\)
Step 6 :Verify the solution by plugging the values of x and y back into the original equations:
Step 7 :For equation 1: \(2x - 5y = 10\)
Step 8 :\(2(5) - 5(0) = 10\)
Step 9 :\(10 = 10\) (True)
Step 10 :For equation 2: \(5y + 6x = 30\)
Step 11 :\(5(0) + 6(5) = 30\)
Step 12 :\(30 = 30\) (True)
Step 13 :\(\boxed{(x, y) = (5, 0)}\)