Question 179040




Start with the given system of equations:


{{{system(x-3y=0,3x+y=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 second equation


{{{3x+y=7}}} Start with the second equation



{{{y=7-3x}}}  Subtract {{{3x}}} from both sides



{{{y=-3x+7}}} Rearrange the equation



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Since {{{y=-3x+7}}}, we can now replace each {{{y}}} in the second equation with {{{-3x+7}}} to solve for {{{x}}}




{{{x-3*highlight((-3x+7))=0}}} Plug in {{{y=-3x+7}}} into the first equation. In other words, replace each {{{y}}} with {{{-3x+7}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+(-3)(-3)x+(-3)(7)=0}}} Distribute {{{-3}}} to {{{-3x+7}}}



{{{x+9x-21=0}}} Multiply



{{{10x-21=0}}} Combine like terms on the left side



{{{10x=0+21}}}Add 21 to both sides



{{{10x=21}}} Combine like terms on the right side



{{{x=21/10}}} Divide both sides by 10 to isolate x





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



So the first part of our answer is: {{{x=21/10}}}



Since we know that {{{x=21/10}}} we can plug it into the equation {{{y=-3x+7}}} (remember we previously solved for {{{y}}} in the second equation).



{{{y=-3x+7}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-3(21/10)+7}}} Plug in {{{x=21/10}}}



{{{y=-63/10+7}}} Multiply



{{{y=7/10}}} 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=7/10}}}








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


So our answers are:


{{{x=21/10}}} and {{{y=7/10}}}


which form the point *[Tex \LARGE \left(\frac{21}{10},\frac{7}{10}\right)]