Question 378670
Note: the first equation is also {{{5x+2y=7}}} (I just rearranged the terms)



Start with the given system of equations:

{{{system(5x+2y=7,2x-4y=10)}}}



{{{2(5x+2y)=2(7)}}} Multiply the both sides of the first equation by 2.



{{{10x+4y=14}}} Distribute and multiply.



So we have the new system of equations:

{{{system(10x+4y=14,2x-4y=10)}}}



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



{{{(10x+4y)+(2x-4y)=(14)+(10)}}}



{{{(10x+2x)+(4y+-4y)=14+10}}} Group like terms.



{{{12x+0y=24}}} Combine like terms.



{{{12x=24}}} Simplify.



{{{x=(24)/(12)}}} Divide both sides by {{{12}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



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{{{10x+4y=14}}} Now go back to the first equation.



{{{10(2)+4y=14}}} Plug in {{{x=2}}}.



{{{20+4y=14}}} Multiply.



{{{4y=14-20}}} Subtract {{{20}}} from both sides.



{{{4y=-6}}} Combine like terms on the right side.



{{{y=(-6)/(4)}}} Divide both sides by {{{4}}} to isolate {{{y}}}.



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



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



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



This means that the system is consistent and independent.



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