Question 325094


Start with the given system of equations:


{{{system(5x+y=30,x+6y=4)}}}




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


{{{5x+y=30}}} Start with the first equation



{{{y=30-5x}}}  Subtract {{{5x}}} from both sides



{{{y=-5x+30}}} Rearrange the equation


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Since {{{y=-5x+30}}}, we can now replace each {{{y}}} in the second equation with {{{-5x+30}}} to solve for {{{x}}}




{{{x+6highlight((-5x+30))=4}}} Plug in {{{y=-5x+30}}} into the second equation. In other words, replace each {{{y}}} with {{{-5x+30}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+(6)(-5)x+(6)(30)=4}}} Distribute {{{6}}} to {{{-5x+30}}}



{{{x-30x+180=4}}} Multiply



{{{-29x+180=4}}} Combine like terms on the left side



{{{-29x=4-180}}}Subtract 180 from both sides



{{{-29x=-176}}} Combine like terms on the right side



{{{x=(-176)/(-29)}}} Divide both sides by -29 to isolate x



{{{x=176/29}}} Reduce



Since we know that {{{x=176/29}}} we can plug it into the equation {{{y=-5x+30}}} (remember we previously solved for {{{y}}} in the first equation).



{{{y=-5x+30}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-5(176/29)+30}}} Plug in {{{x=176/29}}}



{{{y=-880/29+30}}} Multiply



{{{y=-10/29}}} Combine like terms 



So the solutions are {{{x=176/29}}} and {{{y=-10/29}}}



which form the ordered pair *[Tex \LARGE \left(\frac{176}{29},-\frac{10}{29}\right)]