Question 201584


Start with the given system of equations:

{{{system(2x-5y=-14,4x-3y=8)}}}



{{{-2(2x-5y)=-2(-14)}}} Multiply the both sides of the first equation by -2.



{{{-4x+10y=28}}} Distribute and multiply.



So we have the new system of equations:

{{{system(-4x+10y=28,4x-3y=8)}}}



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



{{{(-4x+10y)+(4x-3y)=(28)+(8)}}}



{{{(-4x+4x)+(10y+-3y)=28+8}}} Group like terms.



{{{0x+7y=36}}} Combine like terms.



{{{7y=36}}} Simplify.



{{{y=(36)/(7)}}} Divide both sides by {{{7}}} to isolate {{{y}}}.



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{{{-4x+10y=28}}} Now go back to the first equation.



{{{-4x+10(36/7)=28}}} Plug in {{{y=36/7}}}.



{{{-4x+360/7=28}}} Multiply.



{{{7(-4x+360/cross(7))=7(28)}}} Multiply both sides by the LCD {{{7}}} to clear any fractions.



{{{-28x+360=196}}} Distribute and multiply.



{{{-28x=196-360}}} Subtract {{{360}}} from both sides.



{{{-28x=-164}}} Combine like terms on the right side.



{{{x=(-164)/(-28)}}} Divide both sides by {{{-28}}} to isolate {{{x}}}.



{{{x=41/7}}} Reduce.



So the solutions are {{{x=41/7}}} and {{{y=36/7}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{41}{7},\frac{36}{7}\right)].



This means that the system is consistent and independent.