Question 127285



Start with the given system of equations:


{{{system(4x+6y=15,-x+2y=5)}}}




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=15}}} Start with the first equation



{{{6y=15-4x}}}  Subtract {{{4x}}} from both sides



{{{6y=-4x+15}}} Rearrange the equation



{{{y=(-4x+15)/(6)}}} Divide both sides by {{{6}}}



{{{y=((-4)/(6))x+(15)/(6)}}} Break up the fraction



{{{y=(-2/3)x+5/2}}} Reduce




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Since {{{y=(-2/3)x+5/2}}}, we can now replace each {{{y}}} in the second equation with {{{(-2/3)x+5/2}}} to solve for {{{x}}}




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




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



{{{-x-(4/3)x+10/2=5}}} Multiply



{{{(6)(-1x-(4/3)x+10/2)=(6)(5)}}} 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-8x+30=30}}} Distribute and multiply the LCM to each side




{{{-14x+30=30}}} Combine like terms on the left side



{{{-14x=30-30}}}Subtract 30 from both sides



{{{-14x=0}}} Combine like terms on the right side



{{{x=(0)/(-14)}}} Divide both sides by -14 to isolate x




{{{x=0}}} Divide






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



So the first part of our answer is: {{{x=0}}}










Since we know that {{{x=0}}} we can plug it into the equation {{{y=(-2/3)x+5/2}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=(-2/3)x+5/2}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=(-2/3)(0)+5/2}}} Plug in {{{x=0}}}



{{{y=0/3+5/2}}} Multiply



{{{y=5/2}}} 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=5/2}}}










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


So our answers are:


{{{x=0}}} and {{{y=5/2}}}


which form the point *[Tex \LARGE \left(0,\frac{5}{2}\right)]