Question 192046

{{{0.3x-0.2y=4}}} Start with the first equation.



{{{3x-2y=40}}} Multiply EVERY term by 10 to make every number a whole number



{{{0.5x+0.3y=-7/17}}} Move onto the second equation



{{{17(0.5x)+17(0.3y)=cross(17)(-7/cross(17))}}} Multiply EVERY term by the LCD 17 to clear out the fractions.



{{{8.5x+5.1y=-7}}} Multiply



{{{85x+51y=-70}}} Multiply EVERY term by 10 to make every number a whole number



So we have the system of equations:


{{{system(3x-2y=40,85x+51y=-70)}}}



{{{51(3x-2y)=51(40)}}} Multiply the both sides of the first equation by 51.



{{{153x-102y=2040}}} Distribute and multiply.



{{{2(85x+51y)=2(-70)}}} Multiply the both sides of the second equation by 2.



{{{170x+102y=-140}}} Distribute and multiply.



So we have the new system of equations:

{{{system(153x-102y=2040,170x+102y=-140)}}}



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



{{{(153x-102y)+(170x+102y)=(2040)+(-140)}}}



{{{(153x+170x)+(-102y+102y)=2040+-140}}} Group like terms.



{{{323x+0y=1900}}} Combine like terms.



{{{323x=1900}}} Simplify.



{{{x=(1900)/(323)}}} Divide both sides by {{{323}}} to isolate {{{x}}}.



{{{x=100/17}}} Reduce.



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{{{153x-102y=2040}}} Now go back to the first equation.



{{{153(100/17)-102y=2040}}} Plug in {{{x=100/17}}}.



{{{900-102y=2040}}} Multiply.



{{{-102y=2040-900}}} Subtract {{{900}}} from both sides.



{{{-102y=1140}}} Combine like terms on the right side.



{{{y=(1140)/(-102)}}} Divide both sides by {{{-102}}} to isolate {{{y}}}.



{{{y=-190/17}}} Reduce.




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Answer: 


So the solutions are {{{x=100/17}}} and {{{y=-190/17}}} 


which form the ordered pair *[Tex \LARGE \left(\frac{100}{17},-\frac{190}{17}\right)]