You can
put this solution on YOUR website!I'll do the first two to get you going in the right direction.
# 1
Start with the first equation.
Add 3y to both sides.
Move onto the second equation
Plug in
Distribute.
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.
Go back to the first isolated equation.
Plug in
Multiply.
Combine like terms.
So the solutions are
and
which form the ordered pair (28,7)
This means that the system is consistent and independent.
# 2
Start with the first equation.
Add
to both sides.
Move onto the second equation.
Plug in
.
Multiply.
Combine like terms on the left 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.
So the solutions are
and
which form the ordered pair (1,2)
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)
(