Question 175915


Start with the given system of equations (note: I've rearranged the equations):


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




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


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



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



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



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




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




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



{{{x+3x+3=2}}} Multiply



{{{4x+3=2}}} Combine like terms on the left side



{{{4x=2-3}}}Subtract 3 from both sides



{{{4x=-1}}} Combine like terms on the right side



{{{x=(-1)/(4)}}} Divide both sides by 4 to isolate x




{{{x=-1/4}}} Reduce






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



So the first part of our answer is: {{{x=-1/4}}}










Since we know that {{{x=-1/4}}} we can plug it into the equation {{{y=x+1}}} (remember we previously solved for {{{y}}} in the first equation).




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



{{{y=-1/4+1}}} Plug in {{{x=-1/4}}}



{{{y=3/4}}} Combine like terms  




-----------------Second Answer------------------------------



So the second part of our answer is: {{{y=3/4}}}










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


So our answers are:


{{{x=-1/4}}} and {{{y=3/4}}}


which form the ordered pair *[Tex \LARGE \left(-\frac{1}{4},\frac{3}{4}\right)]