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SOLUTION: solve by the substatution method 2x+4y=26 -2x+y=19 the solution is ___________ __
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Question 407511
:
solve by the substatution method
2x+4y=26
-2x+y=19
the solution is ______________
Answer by
jim_thompson5910(33401)
(
Show Source
):
You can
put this solution on YOUR website!
Start with the given system of equations:
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
Add
to both sides
Rearrange the equation
---------------------
Since
, we can now replace each
in the second equation with
to solve for
Plug in
into the second 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 76 from both sides
Combine like terms on the right side
Divide both sides by 10 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 form the point
Now let's graph the two equations (if you need help with graphing, check out this
solver
)
From the graph, we can see that the two equations intersect at
. This visually verifies our answer.
graph of
(red) and
(green) and the intersection of the lines (blue circle).
If you need more help, email me at
jim_thompson5910@hotmail.com
Also, please consider visiting my website:
http://www.freewebs.com/jimthompson5910/home.html
and making a donation. Thank you
Jim