Question 127880
Do you want to solve using substitution?







Start with the given system of equations:


{{{system(-4x-6y=7,x+5y=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-6y=7}}} Start with the first equation



{{{-6y=7+4x}}} Add {{{4x}}} to both sides



{{{-6y=+4x+7}}} Rearrange the equation



{{{y=(+4x+7)/(-6)}}} Divide both sides by {{{-6}}}



{{{y=((+4)/(-6))x+(7)/(-6)}}} Break up the fraction



{{{y=(-2/3)x-7/6}}} Reduce




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Since {{{y=(-2/3)x-7/6}}}, we can now replace each {{{y}}} in the second equation with {{{(-2/3)x-7/6}}} to solve for {{{x}}}




{{{x+5highlight(((-2/3)x-7/6))=8}}} Plug in {{{y=(-2/3)x-7/6}}} into the first equation. In other words, replace each {{{y}}} with {{{(-2/3)x-7/6}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+(5)(-2/3)x+(5)(-7/6)=8}}} Distribute {{{5}}} to {{{(-2/3)x-7/6}}}



{{{x-(10/3)x-35/6=8}}} Multiply



{{{(6)(1x-(10/3)x-35/6)=(6)(8)}}} Multiply both sides by the LCM of 6. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)




{{{6x-20x-35=48}}} Distribute and multiply the LCM to each side




{{{-14x-35=48}}} Combine like terms on the left side



{{{-14x=48+35}}}Add 35 to both sides



{{{-14x=83}}} Combine like terms on the right side



{{{x=(83)/(-14)}}} Divide both sides by -14 to isolate x




{{{x=-83/14}}} Reduce






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



So the first part of our answer is: {{{x=-83/14}}}










Since we know that {{{x=-83/14}}} we can plug it into the equation {{{y=(-2/3)x-7/6}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=(-2/3)x-7/6}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=(-2/3)(-83/14)-7/6}}} Plug in {{{x=-83/14}}}



{{{y=166/42-7/6}}} Multiply



{{{y=39/14}}} 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=39/14}}}










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


So our answers are:


{{{x=-83/14}}} and {{{y=39/14}}}


which form the point *[Tex \LARGE \left(-\frac{83}{14},\frac{39}{14}\right)]