Question 677171


Start with the given system of equations:

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



{{{2(x-3y)=2(-3)}}} Multiply the both sides of the second equation by 2.



{{{2x-6y=-6}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-2x+2y=-1,2x-6y=-6)}}}



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+2y)+(2x-6y)=(-1)+(-6)}}}



{{{(-2x+2x)+(2y+-6y)=-1+-6}}} Group like terms.



{{{0x+-4y=-7}}} Combine like terms.



{{{-4y=-7}}} Simplify.



{{{y=(-7)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=7/4}}} Reduce.



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{{{-2x+2y=-1}}} Now go back to the first equation.



{{{-2x+2(7/4)=-1}}} Plug in {{{y=7/4}}}.



{{{-2x+7/2=-1}}} Multiply.



{{{2(-2x+7/cross(2))=2(-1)}}} Multiply both sides by the LCD {{{2}}} to clear any fractions.



{{{-4x+7=-2}}} Distribute and multiply.



{{{-4x=-2-7}}} Subtract {{{7}}} from both sides.



{{{-4x=-9}}} Combine like terms on the right side.



{{{x=(-9)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{x}}}.



{{{x=9/4}}} Reduce.



So the solutions are {{{x=9/4}}} and {{{y=7/4}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{9}{4},\frac{7}{4}\right)].



This means that the system is consistent and independent.