Question 143378



Start with the given system of equations:


{{{system(4x-2y=8,2x+4y=8)}}}




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+8}}} Rearrange the equation



{{{y=(-4x+8)/(-2)}}} Divide both sides by {{{-2}}}



{{{y=((-4)/(-2))x+(8)/(-2)}}} 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+4highlight((2x-4))=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+(4)(2)x+(4)(-4)=8}}} Distribute {{{4}}} to {{{2x-4}}}



{{{2x+8x-16=8}}} Multiply



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



{{{10x=8+16}}}Add 16 to both sides



{{{10x=24}}} Combine like terms on the right side



{{{x=(24)/(10)}}} Divide both sides by 10 to isolate x




{{{x=12/5}}} Reduce






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



So the first part of our answer is: {{{x=12/5}}}










Since we know that {{{x=12/5}}} 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(12/5)-4}}} Plug in {{{x=12/5}}}



{{{y=24/5-4}}} Multiply



{{{y=4/5}}} Combine like terms  (note: if you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>)




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



So the second part of our answer is: {{{y=4/5}}}










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


So our answers are:


{{{x=12/5}}} and {{{y=4/5}}}