Question 150797

Start with the given system of equations:


{{{system(5x+4y=14,15x-2y=7)}}}




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+4y=14}}} Start with the first equation



{{{4y=14-5x}}}  Subtract {{{5x}}} from both sides



{{{4y=-5x+14}}} Rearrange the equation



{{{y=(-5x+14)/(4)}}} Divide both sides by {{{4}}}



{{{y=((-5)/(4))x+(14)/(4)}}} Break up the fraction



{{{y=(-5/4)x+7/2}}} Reduce




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Since {{{y=(-5/4)x+7/2}}}, we can now replace each {{{y}}} in the second equation with {{{(-5/4)x+7/2}}} to solve for {{{x}}}




{{{15x-2highlight(((-5/4)x+7/2))=7}}} Plug in {{{y=(-5/4)x+7/2}}} into the first equation. In other words, replace each {{{y}}} with {{{(-5/4)x+7/2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{15x+(-2)(-5/4)x+(-2)(7/2)=7}}} Distribute {{{-2}}} to {{{(-5/4)x+7/2}}}



{{{15x+(10/4)x-14/2=7}}} Multiply



{{{(4)(15x+(10/4)x-14/2)=(4)(7)}}} Multiply both sides by the LCM of 4. 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>)




{{{60x+10x-28=28}}} Distribute and multiply the LCM to each side




{{{70x-28=28}}} Combine like terms on the left side



{{{70x=28+28}}}Add 28 to both sides



{{{70x=56}}} Combine like terms on the right side



{{{x=(56)/(70)}}} Divide both sides by 70 to isolate x




{{{x=4/5}}} Reduce






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



So the first part of our answer is: {{{x=4/5}}}










Since we know that {{{x=4/5}}} we can plug it into the equation {{{y=(-5/4)x+7/2}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=(-5/4)x+7/2}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=(-5/4)(4/5)+7/2}}} Plug in {{{x=4/5}}}



{{{y=-20/20+7/2}}} 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=4/5}}} and {{{y=5/2}}}


which forms the ordered pair *[Tex \LARGE \left(\frac{4}{5},\frac{5}{2}\right)]