3x−2y=3,2x−3y=15
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
3x−2y=3
Add 2y to both sides of the equation.
3x=2y+3
Divide both sides by 3.
x=
3
1
(2y+3)
Multiply
3
1
times 2y+3.
x=
3
2
y+1
Substitute
3
2y
+1 for x in the other equation, 2x−3y=15.
2(
3
2
y+1)−3y=15
Multiply 2 times
3
2y
+1.
3
4
y+2−3y=15
Add
3
4y
to −3y.
−
3
5
y+2=15
Subtract 2 from both sides of the equation.
−
3
5
y=13
Divide both sides of the equation by −
3
5
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=−
5
39
Substitute −
5
39
for y in x=
3
2
y+1. Because the resulting equation contains only one variable, you can solve for x directly.
x=
3
2
(−
5
39
)+1
Multiply
3
2
times −
5
39
by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
x=−
5
26
+1
Add 1 to −
5
26
.
x=−
5
21
The system is now solved.
x=−
5
21
,y=−
5
39