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put this solution on YOUR website!Let x=# of $2 tickets and y=# of $3 tickets
First translate the word problem into the 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
---------------------
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
Combine like terms on the left side
Subtract 1020 from both sides
Combine like terms on the right side
Divide both sides by -1 to isolate x
Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that
we can plug it into the equation
(remember we previously solved for
in the first equation).
Start with the equation where
was previously isolated.
Plug in
Multiply
Combine like terms
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
which means that 210 $2 tickets and 130 $3 tickets were sold
