solve graphically
2x + y =8
x+y=5
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2
Answer:
This could be solved with either elimination or substitution. I'll use elimination, since the category is "Linear Systems with Multiplication."
Multiply the first equation by
−
1
.
−
1
(
x
+
y
=
5
)
→
−
x
−
y
=
−
5
We now have the two equations:
{
−
x
−
y
=
−
5
2
x
+
y
=
8
Add the two equations together.
−
x
+
2
x
−
y
+
y
=
−
5
+
8
Simplify. Notice that the
y
terms cancel, which was the point in multiplying the first equation by
−
1
earlier.
x
=
3
Now, substitute
x
=
3
into either of the original equations.
3
+
y
=
5
y
=
2
This leaves us with
x
=
3
,
y
=
2
, or the point
(
3
,
2
)
.
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