Question 637179


Start with the given system of equations:

{{{system(-3x-10y=9,14x+18y=-22)}}}



{{{9(-3x-10y)=9(9)}}} Multiply the both sides of the first equation by 9.



{{{-27x-90y=81}}} Distribute and multiply.



{{{5(14x+18y)=5(-22)}}} Multiply the both sides of the second equation by 5.



{{{70x+90y=-110}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-27x-90y=81,70x+90y=-110)}}}



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



{{{(-27x-90y)+(70x+90y)=(81)+(-110)}}}



{{{(-27x+70x)+(-90y+90y)=81+-110}}} Group like terms.



{{{43x+0y=-29}}} Combine like terms.



{{{43x=-29}}} Simplify.



{{{x=(-29)/(43)}}} Divide both sides by {{{43}}} to isolate {{{x}}}.



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{{{-27x-90y=81}}} Now go back to the first equation.



{{{-27(-29/43)-90y=81}}} Plug in {{{x=-29/43}}}.



{{{783/43-90y=81}}} Multiply.



{{{43(783/cross(43)-90y)=43(81)}}} Multiply both sides by the LCD {{{43}}} to clear any fractions.



{{{783-3870y=3483}}} Distribute and multiply.



{{{-3870y=3483-783}}} Subtract {{{783}}} from both sides.



{{{-3870y=2700}}} Combine like terms on the right side.



{{{y=(2700)/(-3870)}}} Divide both sides by {{{-3870}}} to isolate {{{y}}}.



{{{y=-30/43}}} Reduce.



So the solutions are {{{x=-29/43}}} and {{{y=-30/43}}}.



Which form the ordered pair *[Tex \LARGE \left(-\frac{29}{43},-\frac{30}{43}\right)].



This means that the system is consistent and independent.