Question 146212


Start with the given system of equations:


{{{system(3x+y=2,-x-3y=6)}}}




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=2}}} Start with the first equation



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



{{{y=-3x+2}}} Rearrange the equation





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




{{{-x-3highlight((-3x+2))=6}}} Plug in {{{y=-3x+2}}} into the first equation. In other words, replace each {{{y}}} with {{{-3x+2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{-x+(-3)(-3)x+(-3)(2)=6}}} Distribute {{{-3}}} to {{{-3x+2}}}



{{{-x+9x-6=6}}} Multiply



{{{8x-6=6}}} Combine like terms on the left side



{{{8x=6+6}}}Add 6 to both sides



{{{8x=12}}} Combine like terms on the right side



{{{x=(12)/(8)}}} Divide both sides by 8 to isolate x




{{{x=3/2}}} Reduce






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



So the first part of our answer is: {{{x=3/2}}}










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




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



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



{{{y=-9/2+2}}} Multiply



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










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


So our answers are:


{{{x=3/2}}} and {{{y=-5/2}}}


which form the ordered pair: *[Tex \LARGE \left(\frac{3}{2},-\frac{5}{2}\right)]