Question 405162
Start with the given system of equations:

{{{system(-4x+y=6,-5x-y=21)}}}



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



{{{(-4x+y)+(-5x-y)=(6)+(21)}}}



{{{(-4x-5x)+(y-y)=6+21}}} Group like terms.



{{{-9x+0y=27}}} Combine like terms. Notice how the y terms cancel out.



{{{-9x=27}}} Simplify.



{{{x=(27)/(-9)}}} Divide both sides by {{{-9}}} to isolate {{{x}}}.



{{{x=-3}}} Reduce.



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{{{-4x+y=6}}} Now go back to the first equation.



{{{-4(-3)+y=6}}} Plug in {{{x=-3}}}.



{{{12+y=6}}} Multiply.



{{{y=6-12}}} Subtract {{{12}}} from both sides.



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



So our answer is {{{x=-3}}} and {{{y=-6}}}.



Which form the ordered pair *[Tex \LARGE \left(-3,-6\right)].



This means that the system is consistent and independent.



Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(-3,-6\right)]. So this visually verifies our answer.



{{{drawing(500,500,-13,7,-16,4,
grid(1),
graph(500,500,-13,7,-16,4,6+4x,(21+5x)/(-1)),
circle(-3,-6,0.05),
circle(-3,-6,0.08),
circle(-3,-6,0.10)
)}}} Graph of {{{-4x+y=6}}} (red) and {{{-5x-y=21}}} (green) 



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