Question 183044



Start with the given system of equations:


{{{system(3x+7y=5,2x-y=1)}}}




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 second equation


{{{2x-y=1}}} Start with the second equation



{{{-y=1-2x}}}  Subtract {{{2x}}} from both sides



{{{-y=-2x+1}}} Rearrange the equation



{{{y=(-2x+1)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=((-2)/(-1))x+(1)/(-1)}}} Break up the fraction



{{{y=2x-1}}} Reduce




---------------------


Since {{{y=2x-1}}}, we can now replace each {{{y}}} in the first equation with {{{2x-1}}} to solve for {{{x}}}




{{{3x+7highlight((2x-1))=5}}} Plug in {{{y=2x-1}}} into the first equation. In other words, replace each {{{y}}} with {{{2x-1}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{3x+(7)(2)x+(7)(-1)=5}}} Distribute {{{7}}} to {{{2x-1}}}



{{{3x+14x-7=5}}} Multiply



{{{17x-7=5}}} Combine like terms on the left side



{{{17x=5+7}}}Add 7 to both sides



{{{17x=12}}} Combine like terms on the right side



{{{x=(12)/(17)}}} Divide both sides by 17 to isolate x





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



So the first part of our answer is: {{{x=12/17}}}










Since we know that {{{x=12/17}}} we can plug it into the equation {{{y=2x-1}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=2x-1}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=2(12/17)-1}}} Plug in {{{x=12/17}}}



{{{y=24/17-1}}} Multiply



{{{y=7/17}}} Combine like terms  (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=7/17}}}










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


So our answers are:


{{{x=12/17}}} and {{{y=7/17}}}


which form the ordered pair *[Tex \LARGE \left(\frac{12}{17},\frac{7}{17}\right)]