Question 252508
The multiplier is 7 since this will change -y into -7y. Add this to 7y to get -7+7y=0y=0 which means that it cancels out.





Start with the given system of equations:

{{{system(3x-y=7,2x+7y=42)}}}



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



{{{21x-7y=49}}} Distribute and multiply.



So we have the new system of equations:

{{{system(21x-7y=49,2x+7y=42)}}}



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



{{{(21x-7y)+(2x+7y)=(49)+(42)}}}



{{{(21x+2x)+(-7y+7y)=49+42}}} Group like terms.



{{{23x+0y=91}}} Combine like terms.



{{{23x=91}}} Simplify.



{{{x=(91)/(23)}}} Divide both sides by {{{23}}} to isolate {{{x}}}.



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{{{21x-7y=49}}} Now go back to the first equation.



{{{21(91/23)-7y=49}}} Plug in {{{x=91/23}}}.



{{{1911/23-7y=49}}} Multiply.



{{{23(1911/cross(23)-7y)=23(49)}}} Multiply both sides by the LCD {{{23}}} to clear any fractions.



{{{1911-161y=1127}}} Distribute and multiply.



{{{-161y=1127-1911}}} Subtract {{{1911}}} from both sides.



{{{-161y=-784}}} Combine like terms on the right side.



{{{y=(-784)/(-161)}}} Divide both sides by {{{-161}}} to isolate {{{y}}}.



{{{y=112/23}}} Reduce.



So the solutions are {{{x=91/23}}} and {{{y=112/23}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{91}{23},\frac{112}{23}\right)].



This means that the system is consistent and independent.