Question 146956


Start with the given system of equations:


{{{system(4x+y=4,2x+8y=0)}}}




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+y=4}}} Start with the first equation



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



{{{y=-4x+4}}} Rearrange the equation





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




{{{2x+8highlight((-4x+4))=0}}} Plug in {{{y=-4x+4}}} into the second equation. In other words, replace each {{{y}}} with {{{-4x+4}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{2x+(8)(-4)x+(8)(4)=0}}} Distribute {{{8}}} to {{{-4x+4}}}



{{{2x-32x+32=0}}} Multiply



{{{-30x+32=0}}} Combine like terms on the left side



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



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



{{{x=(-32)/(-30)}}} Divide both sides by -30 to isolate x




{{{x=16/15}}} Reduce






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



So the first part of our answer is: {{{x=16/15}}}










Since we know that {{{x=16/15}}} we can plug it into the equation {{{y=-4x+4}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-4x+4}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-4(16/15)+4}}} Plug in {{{x=16/15}}}



{{{y=-64/15+4}}} Multiply



{{{y=-4/15}}} 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=-4/15}}}










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


So our answers are:


{{{x=16/15}}} and {{{y=-4/15}}}


which form the ordered pair *[Tex \LARGE \left(\frac{16}{15},-\frac{4}{15}\right)]