Question 555472

Start with the given system of equations:

{{{system(6x-y=-4,2x+2y=-2)}}}



{{{2(6x-y)=2(-4)}}} Multiply the both sides of the first equation by 2.



{{{12x-2y=-8}}} Distribute and multiply.



So we have the new system of equations:

{{{system(12x-2y=-8,2x+2y=-2)}}}



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



{{{(12x-2y)+(2x+2y)=(-8)+(-2)}}}



{{{(12x+2x)+(-2y+2y)=-8+-2}}} Group like terms.



{{{14x+0y=-10}}} Combine like terms.



{{{14x=-10}}} Simplify.



{{{x=(-10)/(14)}}} Divide both sides by {{{14}}} to isolate {{{x}}}.



{{{x=-5/7}}} Reduce.



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{{{12x-2y=-8}}} Now go back to the first equation.



{{{12(-5/7)-2y=-8}}} Plug in {{{x=-5/7}}}.



{{{-60/7-2y=-8}}} Multiply.



{{{7(-60/cross(7)-2y)=7(-8)}}} Multiply both sides by the LCD {{{7}}} to clear any fractions.



{{{-60-14y=-56}}} Distribute and multiply.



{{{-14y=-56+60}}} Add {{{60}}} to both sides.



{{{-14y=4}}} Combine like terms on the right side.



{{{y=(4)/(-14)}}} Divide both sides by {{{-14}}} to isolate {{{y}}}.



{{{y=-2/7}}} Reduce.



So the solutions are {{{x=-5/7}}} and {{{y=-2/7}}}.



Which form the ordered pair *[Tex \LARGE \left(-\frac{5}{7},-\frac{2}{7}\right)].



This means that the system is consistent and independent.



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