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Start with the given system of equations:
Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms. Notice how the y terms cancel out.
Simplify.
Divide both sides by
to isolate
.
Reduce.
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Now go back to the first equation.
Plug in
.
Multiply.
Subtract
from both sides.
Combine like terms on the right side.
Divide both sides by
to isolate
.
Reduce.
So our answer is
and
.
Which form the ordered pair
)
. Good job. As a check, simply plug in
and
and you should get two identities.
This means that the system is consistent and independent.
Notice when we graph the equations, we see that they intersect at
. So this visually verifies our answer.
Graph of
(red) and
(green)
(