x + 5 = 3y, 4x + y = 2
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Your system of equations looks like this
{
4
x
−
y
=
−
5
−
2
x
+
3
y
=
10
Multiply the second equation by
2
to get
{
4
x
−
y
=
−
5
−
4
x
+
6
y
=
20
Notice that if you add the left-hand side of the equations and the right-hand sides of the equations separately, you can eliminate the
x
-term.
This will allow you to find the value of
y
, since you'll be left with one equation with one unknown,
y
.
{
4
x
−
y
=
−
5
−
4
x
+
6
y
=
20
--------------------------------------------
4
x
−
y
−
4
x
+
6
y
=
−
5
+
20
5
y
=
15
⇒
y
=
3
Now take the value of
y
into one of the two original equations to solve for
x
4
x
−
3
=
−
5
4
x
=
−
2
⇒
x
=
−
1
2
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