Question 165385
Start with the given system of equations:


{{{system(12x+y=21,18x-3y=-36)}}}




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


{{{12x+y=21}}} Start with the first equation



{{{y=21-12x}}}  Subtract {{{12x}}} from both sides



{{{y=-12x+21}}} Rearrange the equation



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Since {{{y=-12x+21}}}, we can now replace each {{{y}}} in the second equation with {{{-12x+21}}} to solve for {{{x}}}




{{{18x-3highlight((-12x+21))=-36}}} Plug in {{{y=-12x+21}}} into the second equation. In other words, replace each {{{y}}} with {{{-12x+21}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{18x+(-3)(-12)x+(-3)(21)=-36}}} Distribute {{{-3}}} to {{{-12x+21}}}



{{{18x+36x-63=-36}}} Multiply



{{{54x-63=-36}}} Combine like terms on the left side



{{{54x=-36+63}}}Add 63 to both sides



{{{54x=27}}} Combine like terms on the right side



{{{x=(27)/(54)}}} Divide both sides by 54 to isolate x




{{{x=1/2}}} Reduce






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



So the first part of our answer is: {{{x=1/2}}}










Since we know that {{{x=1/2}}} we can plug it into the equation {{{y=-12x+21}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-12x+21}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-12(1/2)+21}}} Plug in {{{x=1/2}}}



{{{y=-12/2+21}}} Multiply



{{{y=15}}} Combine like terms and reduce.  (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=15}}}










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


So our answers are:


{{{x=1/2}}} and {{{y=15}}}


which form the ordered pair *[Tex \LARGE \left(\frac{1}{2},15\right)]