2x + 3y = 20
x + 2y = 11.25
multiply the second equation by -2 on both sides
2x + 3y = 20
-2x - 4y = -22.5
add the equations straight down
0x - y = -2.5
divide both sides by -1
0x + y = 2.5
y = 2.5
Put y = 2.5 into one of the original equations.
x + 2y = 11.25
x + 2(2.5) = 11.25
x + 5 = 11.25
x = 6.25
Answer: x = 6.25, y = 2.5