Question 398681



Start with the given system of equations:


{{{system(-2x+y=-2,x-4y=9)}}}




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


{{{-2x+y=-2}}} Start with the first equation



{{{y=-2+2x}}} Add {{{2x}}} to both sides



{{{y=2x-2}}} Rearrange the equation


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


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




{{{x-4highlight((2x-2))=9}}} Plug in {{{y=2x-2}}} into the second equation. In other words, replace each {{{y}}} with {{{2x-2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+(-4)(2)x+(-4)(-2)=9}}} Distribute {{{-4}}} to {{{2x-2}}}



{{{x-8x+8=9}}} Multiply



{{{-7x+8=9}}} Combine like terms on the left side



{{{-7x=9-8}}}Subtract 8 from both sides



{{{-7x=1}}} Combine like terms on the right side



{{{x=(1)/(-7)}}} Divide both sides by -7 to isolate x




{{{x=-1/7}}} Reduce






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



So the first part of our answer is: {{{x=-1/7}}}










Since we know that {{{x=-1/7}}} we can plug it into the equation {{{y=2x-2}}} (remember we previously solved for {{{y}}} in the first equation).




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



{{{y=2(-1/7)-2}}} Plug in {{{x=-1/7}}}



{{{y=-2/7-2}}} Multiply



{{{y=-16/7}}} 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=-16/7}}}










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


So our answers are:


{{{x=-1/7}}} and {{{y=-16/7}}}


which form the point *[Tex \LARGE \left(-\frac{1}{7},-\frac{16}{7}\right)] 




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