3x − y = 2; x + 2y = 3
Solve 3x − y = 2 for y:
Add -3x to both sides
3x − y + −3x = 2 + −3x
−y = −3x + 2
Divide both sides by -1
−y −1 = −3x + 2 − 1
y = 3x − 2
Substitute 3x − 2 for y in x + 2y = 3:
x + 2y = 3
x + 2(3x−2) = 3
Simplify both sides of the equation
7x − 4 = 3
Add 4 to both sides
7x − 4 + 4 = 3 + 4
7x = 7
Divide both sides by 7
7x/7 = 7/7
x = 1
Substitute 1 for x in y = 3x − 2:
y = 3x − 2
y = (3)(1) − 2
Simplify both sides of the equation
y = 1
Answer:
x = 1 and y = 1