Question 678297
I'm going to use elimination.




Start with the given system of equations:

{{{system(2x-6y=5,x+y=2)}}}



{{{6(x+y)=6(2)}}} Multiply the both sides of the second equation by 6.



{{{6x+6y=12}}} Distribute and multiply.



So we have the new system of equations:

{{{system(2x-6y=5,6x+6y=12)}}}



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-6y)+(6x+6y)=(5)+(12)}}}



{{{(2x+6x)+(-6y+6y)=5+12}}} Group like terms.



{{{8x+0y=17}}} Combine like terms.



{{{8x=17}}} Simplify.



{{{x=(17)/(8)}}} Divide both sides by {{{8}}} to isolate {{{x}}}.



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{{{2x-6y=5}}} Now go back to the first equation.



{{{2(17/8)-6y=5}}} Plug in {{{x=17/8}}}.



{{{17/4-6y=5}}} Multiply.



{{{4(17/cross(4)-6y)=4(5)}}} Multiply both sides by the LCD {{{4}}} to clear any fractions.



{{{17-24y=20}}} Distribute and multiply.



{{{-24y=20-17}}} Subtract {{{17}}} from both sides.



{{{-24y=3}}} Combine like terms on the right side.



{{{y=(3)/(-24)}}} Divide both sides by {{{-24}}} to isolate {{{y}}}.



{{{y=-1/8}}} Reduce.



So the solutions are {{{x=17/8}}} and {{{y=-1/8}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{17}{8},-\frac{1}{8}\right)].



This means that the system is consistent and independent.