SOLUTION: solve the system using the substitution method. present as an ordered method. If not, specify whether the answer is no solution or infinite many solution 4x + y=4 2x + 8y=0

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Question 146956: solve the system using the substitution method. present as an ordered method. If not, specify whether the answer is no solution or infinite many solution
4x + y=4
2x + 8y=0
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%2By=4%2C2x%2B8y=0%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%2By=4 Start with the first equation


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


y=-4x%2B4 Rearrange the equation




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

Since y=-4x%2B4, we can now replace each y in the second equation with -4x%2B4 to solve for x



2x%2B8highlight%28%28-4x%2B4%29%29=0 Plug in y=-4x%2B4 into the second equation. In other words, replace each y with -4x%2B4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%288%29%28-4%29x%2B%288%29%284%29=0 Distribute 8 to -4x%2B4


2x-32x%2B32=0 Multiply


-30x%2B32=0 Combine like terms on the left side


-30x=0-32Subtract 32 from both sides


-30x=-32 Combine like terms on the right side


x=%28-32%29%2F%28-30%29 Divide both sides by -30 to isolate x



x=16%2F15 Reduce





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


So the first part of our answer is: x=16%2F15









Since we know that x=16%2F15 we can plug it into the equation y=-4x%2B4 (remember we previously solved for y in the first equation).



y=-4x%2B4 Start with the equation where y was previously isolated.


y=-4%2816%2F15%29%2B4 Plug in x=16%2F15


y=-64%2F15%2B4 Multiply


y=-4%2F15 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%2F15









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

So our answers are:

x=16%2F15 and y=-4%2F15

which form the ordered pair