Question 529790


Start with the given system of equations:

{{{system(7x+6y=30,9x-8y=15)}}}



{{{8(7x+6y)=8(30)}}} Multiply the both sides of the first equation by 8.



{{{56x+48y=240}}} Distribute and multiply.



{{{6(9x-8y)=6(15)}}} Multiply the both sides of the second equation by 6.



{{{54x-48y=90}}} Distribute and multiply.



So we have the new system of equations:

{{{system(56x+48y=240,54x-48y=90)}}}



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



{{{(56x+48y)+(54x-48y)=(240)+(90)}}}



{{{(56x+54x)+(48y+-48y)=240+90}}} Group like terms.



{{{110x+0y=330}}} Combine like terms.



{{{110x=330}}} Simplify.



{{{x=(330)/(110)}}} Divide both sides by {{{110}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



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{{{56x+48y=240}}} Now go back to the first equation.



{{{56(3)+48y=240}}} Plug in {{{x=3}}}.



{{{168+48y=240}}} Multiply.



{{{48y=240-168}}} Subtract {{{168}}} from both sides.



{{{48y=72}}} Combine like terms on the right side.



{{{y=(72)/(48)}}} Divide both sides by {{{48}}} to isolate {{{y}}}.



{{{y=3/2}}} Reduce.



So the solutions are {{{x=3}}} and {{{y=3/2}}}.



Which form the ordered pair *[Tex \LARGE \left(3,\frac{3}{2}\right)].



This means that the system is consistent and independent.



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