Let's solve your system by substitution.
2
x
−
3
y
=
1
;
3
x
+
2
y
=
6
Step: Solve
2
x
−
3
y
=
1
for x:
2
x
−
3
y
=
1
2
x
−
3
y
+
3
y
=
1
+
3
y
(Add 3y to both sides)
2
x
=
3
y
+
1
2
x
2
=
3
y
+
1
2
(Divide both sides by 2)
x
=
3
2
y
+
1
2
Step: Substitute
3
2
y
+
1
2
for
x
in
3
x
+
2
y
=
6
:
3
x
+
2
y
=
6
3
(
3
2
y
+
1
2
)
+
2
y
=
6
13
2
y
+
3
2
=
6
(Simplify both sides of the equation)
13
2
y
+
3
2
+
−
3
2
=
6
+
−
3
2
(Add (-3)/2 to both sides)
13
2
y
=
9
2
13
2
y
13
2
=
9
2
13
2
(Divide both sides by 13/2)
y
=
9
13
Step: Substitute
9
13
for
y
in
x
=
3
2
y
+
1
2
:
x
=
3
2
y
+
1
2
x
=
3
2
(
9
13
)
+
1
2
x
=
20
13
(Simplify both sides of the equation)
Answer:
x
=
20
13
and
y
=
9
13
