Question 591322


Start with the given system of equations:

{{{system(3x+4y=5,2x+y=1)}}}



{{{-4(2x+y)=-4(1)}}} Multiply the both sides of the second equation by -4.



{{{-8x-4y=-4}}} Distribute and multiply.



So we have the new system of equations:

{{{system(3x+4y=5,-8x-4y=-4)}}}



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



{{{(3x+4y)+(-8x-4y)=(5)+(-4)}}}



{{{(3x+-8x)+(4y+-4y)=5+-4}}} Group like terms.



{{{-5x+0y=1}}} Combine like terms.



{{{-5x=1}}} Simplify.



{{{x=(1)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}.



{{{x=-1/5}}} Reduce.



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{{{3x+4y=5}}} Now go back to the first equation.



{{{3(-1/5)+4y=5}}} Plug in {{{x=-1/5}}}.



{{{-3/5+4y=5}}} Multiply.



{{{5(-3/cross(5)+4y)=5(5)}}} Multiply both sides by the LCD {{{5}}} to clear any fractions.



{{{-3+20y=25}}} Distribute and multiply.



{{{20y=25+3}}} Add {{{3}}} to both sides.



{{{20y=28}}} Combine like terms on the right side.



{{{y=(28)/(20)}}} Divide both sides by {{{20}}} to isolate {{{y}}}.



{{{y=7/5}}} Reduce.



So the solutions are {{{x=-1/5}}} and {{{y=7/5}}}.



Which form the ordered pair *[Tex \LARGE \left(-\frac{1}{5},\frac{7}{5}\right)].



This means that the system is consistent and independent.