Question 324151


Start with the given system of equations:

{{{system(8x-4y=12,2x-8y=3)}}}



{{{-2(8x-4y)=-2(12)}}} Multiply the both sides of the first equation by -2.



{{{-16x+8y=-24}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-16x+8y=-24,2x-8y=3)}}}



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



{{{(-16x+8y)+(2x-8y)=(-24)+(3)}}}



{{{(-16x+2x)+(8y+-8y)=-24+3}}} Group like terms.



{{{-14x+0y=-21}}} Combine like terms.



{{{-14x=-21}}} Simplify.



{{{x=(-21)/(-14)}}} Divide both sides by {{{-14}}} to isolate {{{x}}}.



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



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{{{-16x+8y=-24}}} Now go back to the first equation.



{{{-16(3/2)+8y=-24}}} Plug in {{{x=3/2}}}.



{{{-24+8y=-24}}} Multiply.



{{{8y=-24+24}}} Add {{{24}}} to both sides.



{{{8y=0}}} Combine like terms on the right side.



{{{y=(0)/(8)}}} Divide both sides by {{{8}}} to isolate {{{y}}}.



{{{y=0}}} Reduce.



So the solutions are {{{x=3/2}}} and {{{y=0}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{3}{2},0\right)].



This means that the system is consistent and independent.