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Start with the given system of equations:
Multiply the both sides of the second equation by -1.
Distribute and multiply.
So we have the new system of equations:
Now 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 x 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.
Add
to 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
)
.
This means that the system is consistent and independent.
So the answer is choice d) (3,-4); consistent/independent
Notice when we graph the equations, we see that they intersect at
. So this visually verifies our answer.
Graph of
(red) and
(green)
(