Question 192047

{{{8x-9y=24.5}}} Start with the first equation.



{{{80x-90y=245}}} Multiply EVERY term by 10 to make every number a whole number



{{{7y-2x=-8.5}}} Move onto the second equation



{{{-2x+7y=-8.5}}} Rearrange the terms.



{{{-20x+70y=-85}}} Multiply EVERY term by 10 to make every number a whole number



So we have the system of equations:

{{{system(80x-90y=245,-20x+70y=-85)}}}



{{{4(-20x+70y)=4(-85)}}} Multiply the both sides of the second equation by 4.



{{{-80x+280y=-340}}} Distribute and multiply.



So we have the new system of equations:

{{{system(80x-90y=245,-80x+280y=-340)}}}



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



{{{(80x-90y)+(-80x+280y)=(245)+(-340)}}}



{{{(80x+-80x)+(-90y+280y)=245+-340}}} Group like terms.



{{{0x+190y=-95}}} Combine like terms.



{{{190y=-95}}} Simplify.



{{{y=(-95)/(190)}}} Divide both sides by {{{190}}} to isolate {{{y}}}.



{{{y=-1/2}}} Reduce.



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{{{80x-90y=245}}} Now go back to the first equation.



{{{80x-90(-1/2)=245}}} Plug in {{{y=-1/2}}}.



{{{80x+45=245}}} Multiply.



{{{80x=245-45}}} Subtract {{{45}}} from both sides.



{{{80x=200}}} Combine like terms on the right side.



{{{x=(200)/(80)}}} Divide both sides by {{{80}}} to isolate {{{x}}}.



{{{x=5/2}}} Reduce.



So the solutions are {{{x=5/2}}} and {{{y=-1/2}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{5}{2},-\frac{1}{2}\right)].



This means that the system is consistent and independent.