You can
put this solution on YOUR website!# 1
Your first equation has two "x" variables. Is there a "y" term in the first equation?
# 2
Start with the given system of equations:
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. Notice how the y terms cancel out.
Simplify.
Divide both sides by
to isolate
.
Reduce.
------------------------------------------------------------------
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)
# 3
Start with the given system of equations:
Multiply the both sides of the first 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.
------------------------------------------------------------------
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)
