2x - 3y = 3
x + 2y = 5
In the second equation we have an x-term that has a coefficient of 1 (which means the x is all by itself), so we can isolate that x and solve by substitution.
x + 2y = 5
x + 2y - 2y = 5 - 2y
x = 5 - 2y
The expression 5 - 2y will be substituted for x in the first equation.
2x - 3y = 3
2(5 - 2y) - 3y = 3
Solve for y.
2(5 - 2y) - 3y = 3
10 - 4y - 3y = 3 (distribute the 2)
10 - 7y = 3 (collect like terms)
-7y = -7 (subtract 10 from both sides)
y = 1 (divide both sides by -7)
Substitute 1 for y in the second equation to find x.
x + 2y = 5
x + 2(1) = 5
Solve for x.
x + 2(1) = 5
x + 2 = 5 (multiply)
x = 3 (subtract 2 from both sides)
Always check your work. Substitute into the original system.
2x - 3y = 3
2(3) - 3(1) = 3
6 - 3 = 3
3 = 3
x + 2y = 5
3 + 2(1) = 5
3 + 2 = 5
5 = 5
x = 3 and y = 1; (3,1)
