Question 133146



Start with the given system of equations:


{{{system(-3x+y=1,5x+2y=-4)}}}




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


{{{-3x+y=1}}} Start with the first equation



{{{y=1+3x}}} Add {{{3x}}} to both sides



{{{y=+3x+1}}} Rearrange the equation



{{{y=(+3x+1)/(1)}}} Divide both sides by {{{1}}}



{{{y=((+3)/(1))x+(1)/(1)}}} Break up the fraction



{{{y=3x+1}}} Reduce




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Since {{{y=3x+1}}}, we can now replace each {{{y}}} in the second equation with {{{3x+1}}} to solve for {{{x}}}




{{{5x+2highlight((3x+1))=-4}}} Plug in {{{y=3x+1}}} into the first equation. In other words, replace each {{{y}}} with {{{3x+1}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{5x+(2)(3)x+(2)(1)=-4}}} Distribute {{{2}}} to {{{3x+1}}}



{{{5x+6x+2=-4}}} Multiply



{{{11x+2=-4}}} Combine like terms on the left side



{{{11x=-4-2}}}Subtract 2 from both sides



{{{11x=-6}}} Combine like terms on the right side



{{{x=(-6)/(11)}}} Divide both sides by 11 to isolate x




{{{x=-6/11}}} Reduce






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



So the first part of our answer is: {{{x=-6/11}}}










Since we know that {{{x=-6/11}}} we can plug it into the equation {{{y=3x+1}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=3x+1}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=3(-6/11)+1}}} Plug in {{{x=-6/11}}}



{{{y=-18/11+1}}} Multiply



{{{y=-7/11}}} 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=-7/11}}}










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


So our answers are:


{{{x=-6/11}}} and {{{y=-7/11}}}


which form the point *[Tex \LARGE \left(-\frac{6}{11},-\frac{7}{11}\right)]