{
x
=
1
y
=
4
Explanation:
Take a look at your starting system of equations
{
5
x
+
y
=
9
10
x
−
7
y
=
−
18
Notice that if you multiply the first equation by
(
−
2
)
, and add the right-hand sides and the left-hand sides of the equations separately, you can eliminate the
x
-term.
This will leave you with one equation with one unknown,
y
.
{
5
x
+
y
=
9
∣
⋅
(
−
2
)
10
x
−
7
y
=
−
18
{
−
10
x
−
2
y
=
−
18
10
x
−
7
y
=
−
18
---------------------------------------------------
−
10
x
−
2
y
+
10
x
−
7
y
=
−
18
+
(
−
18
)
−
9
y
=
−
36
⇒
y
=
(
−
36
)
(
−
9
)
=
4
Now use this value of
y
in one of the two original equations to find the value of
x
5
x
+
(
4
)
=
9
5
x
=
5
⇒
x
=
5
5
=
1
