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Start with the first equation.
Multiply both sides by the LCD
to clear any fractions.
Distribute and multiply.
Move onto the second equation.
Multiply both sides by the LCD
to clear any fractions.
Distribute and multiply.
So we have the system of equations:
Multiply the both sides of the second equation by -3.
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.
Notice when we graph the equations, we see that they intersect at
. So this visually verifies our answer.
Graph of
(red) and
(green)
