2x - 3y = 3

x + 2y = 5

by substitution or elimination

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

Answer:

x = 3 and y = 1; (3,1)