Question 158049
I'm going to use the elimination method





Start with the given system of equations:



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



{{{3(7x-y)=3(3)}}} Multiply the both sides of the second equation by 3.



{{{21x-3y=9}}} Distribute and multiply.



So we have the new system of equations:

{{{system(2x+3y=2,21x-3y=9)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(2x+3y)+(21x-3y)=(2)+(9)}}}



{{{(2x+21x)+(3y-3y)=2+9}}} Group like terms.



{{{23x+0y=11}}} Combine like terms. Notice how the y terms cancel out.



{{{23x=11}}} Simplify.



{{{x=(11)/(23)}}} Divide both sides by {{{23}}} to isolate {{{x}}}.



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{{{2x+3y=2}}} Now go back to the first equation.



{{{2(11/23)+3y=2}}} Plug in {{{x=11/23}}}.



{{{22/23+3y=2}}} Multiply.



{{{22+69y=46}}} Multiply <b>EVERY</b> term by the LCD 23 to clear the fraction



{{{69y=46-22}}} Subtract {{{22}}} from both sides.



{{{69y=24}}} Combine like terms on the right side.



{{{y=(24)/(69)}}} Divide both sides by {{{69}}} to isolate {{{y}}}.



{{{y=8/23}}} Reduce.



So the solutions are {{{x=(11)/(23)}}} and {{{y=8/23}}}