2x + 3y = 12 Equation 1
3x + 2y = 13 Equation 2
2x + 3y = 12
2x = 12 - 3y
x = 6 - (3/2)y Equation 3
Substituting Equation 3 into Equation 2:
3[6 - (3/2)y] + 2y = 12 Original Problem.
18 - 4.5y + 2y = 13 Distribute.
-4.5y + 2y = -5 Subtract 18 from each side.
-2.5y = -5 Add.
y = 2 Divide each side by -2.5
Substituting value of y into Equation 1:
2x + 3(2) = 12 Original Problem.
2x + 6 = 12 Multiply.
2x = 6 Subtract 6 from each side.
x = 3 Divide each side by 2.
Answer: x = 3 and y = 2