2
x
+
3
y
=
1
2
x
+
3
y
=
1
,
−
2
x
−
3
y
=
−
1
-
2
x
-
3
y
=
-
1
Solve for
y
y
in the second equation.
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2
x
+
3
y
=
1
2
x
+
3
y
=
1
y
=
−
2
x
3
+
1
3
y
=
-
2
x
3
+
1
3
Replace all occurrences of
y
y
with the solution found by solving the last equation for
y
y
. In this case, the value substituted is
−
2
x
3
+
1
3
-
2
x
3
+
1
3
.
2
x
+
3
(
−
2
x
3
+
1
3
)
=
1
2
x
+
3
(
-
2
x
3
+
1
3
)
=
1
y
=
−
2
x
3
+
1
3
y
=
-
2
x
3
+
1
3
Solve for
x
x
in the first equation.
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Always true
y
=
−
2
x
3
+
1
3
y
=
-
2
x
3
+
1
3
Remove any equations from the system that are always true.
y
=
−
2
x
3
+
1
3
y
=
-
2
x
3
+
1
3
The solution can be shown in both point and equation forms.
Point Form:
(
x
,
−
2
x
3
+
1
3
)
(
x
,
-
2
x
3
+
1
3
)
Equation Form:
x
=
x
y
=
−
2
x
3
+
1
3