SOLUTION: This one is really confusing me, I need some help. Solve the following system by substitution. 4x - 2y = 8 2x + 4y =8

Algebra ->  Systems-of-equations -> SOLUTION: This one is really confusing me, I need some help. Solve the following system by substitution. 4x - 2y = 8 2x + 4y =8       Log On


   

Question 143378: This one is really confusing me, I need some help.
Solve the following system by substitution.

4x - 2y = 8
2x + 4y =8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system%284x-2y=8%2C2x%2B4y=8%29



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

4x-2y=8 Start with the first equation


-2y=8-4x Subtract 4x from both sides


-2y=-4x%2B8 Rearrange the equation


y=%28-4x%2B8%29%2F%28-2%29 Divide both sides by -2


y=%28%28-4%29%2F%28-2%29%29x%2B%288%29%2F%28-2%29 Break up the fraction


y=2x-4 Reduce



---------------------

Since y=2x-4, we can now replace each y in the second equation with 2x-4 to solve for x



2x%2B4highlight%28%282x-4%29%29=8 Plug in y=2x-4 into the first equation. In other words, replace each y with 2x-4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%284%29%282%29x%2B%284%29%28-4%29=8 Distribute 4 to 2x-4


2x%2B8x-16=8 Multiply


10x-16=8 Combine like terms on the left side


10x=8%2B16Add 16 to both sides


10x=24 Combine like terms on the right side


x=%2824%29%2F%2810%29 Divide both sides by 10 to isolate x



x=12%2F5 Reduce





-----------------First Answer------------------------------


So the first part of our answer is: x=12%2F5









Since we know that x=12%2F5 we can plug it into the equation y=2x-4 (remember we previously solved for y in the first equation).



y=2x-4 Start with the equation where y was previously isolated.


y=2%2812%2F5%29-4 Plug in x=12%2F5


y=24%2F5-4 Multiply


y=4%2F5 Combine like terms (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is: y=4%2F5









-----------------Summary------------------------------

So our answers are:

x=12%2F5 and y=4%2F5