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# 1
Start with the given system of equations:
Start with the first equation.
Add
to both sides.
Divide both sides by
to isolate
.
Simplify.
-------------------------------------------
Now plug in
into the second equation.
Multiply.
Multiply both sides by the LCD
to clear any fractions.
Distribute and multiply.
Combine like terms on the left side.
Add
to both sides.
Combine like terms on the right side.
Divide both sides by
to isolate
.
Reduce.
-------------------------------------------
Since we know that
, we can use this to find
.
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 the answer is
and
.
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)
