Question 585447

Start with the given system of equations:

{{{system(6x-y=-8,2x+y=-16)}}}



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



{{{(6x-y)+(2x+y)=(-8)+(-16)}}}



{{{(6x+2x)+(-y+y)=-8+-16}}} Group like terms.



{{{8x+0y=-24}}} Combine like terms.



{{{8x=-24}}} Simplify.



{{{x=(-24)/(8)}}} Divide both sides by {{{8}}} to isolate {{{x}}}.



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



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{{{6x-1y=-8}}} Now go back to the first equation.



{{{6(-3)-1y=-8}}} Plug in {{{x=-3}}}.



{{{-18-y=-8}}} Multiply.



{{{-y=-8+18}}} Add {{{18}}} to both sides.



{{{-y=10}}} Combine like terms on the right side.



{{{y=(10)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=-10}}} Reduce.



So the solutions are {{{x=-3}}} and {{{y=-10}}}.



Which form the ordered pair *[Tex \LARGE \left(-3,-10\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,-10\right)]. So this visually verifies our answer.



{{{drawing(500,500,-13,7,-15,5,
grid(1),
graph(500,500,-13,7,-15,5,(-8-6x)/(-1),-16-2x),
circle(-3,-10,0.05),
circle(-3,-10,0.08),
circle(-3,-10,0.10)
)}}} Graph of {{{6x-y=-8}}} (red) and {{{2x+y=-16}}} (green) 



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