You can
put this solution on YOUR website!I'll do the first two to get you started:
1)
Start with the given system of equations:
Let's use substitution to solve the system
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
Subtract
from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
---------------------
Since
, we can now replace each
in the second equation with
to solve for
Plug in
into the first equation. In other words, replace each
with
. Notice we've eliminated the
variables. So we now have a simple equation with one unknown.
Distribute
to
Multiply
Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this
solver)
Distribute and multiply the LCM to each side
Combine like terms on the left side
Add 64 to both sides
Combine like terms on the right side
Simplify
Since this equation is
never true for any x value, this means there are no solutions.
2)
Start with the given system of equations:
Let's use elimination to solve the system
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
Divide both sides by -5.
So our answer is
and
.
Which form the ordered pair
)
.
