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Start with the given system of equations:
Multiply the both sides of the first equation by 2.
Distribute and multiply.
Multiply the both sides of the second equation by 5.
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.
Simplify.
Divide both sides by
to isolate
.
Reduce.
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Now go back to the first equation.
Plug in
.
Multiply.
Multiply EVERY term by the LCD
to clear any fractions.
Multiply.
Subtract
from both sides.
Combine like terms on the right side.
Divide both sides by
to isolate
.
Reduce.
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Answer:
So the solutions are
and
which form the ordered pair
)
(