Question 548770

Start with the given system of equations:

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



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



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



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



{{{0x-4y=-12}}} Combine like terms.



{{{-4y=-12}}} Simplify.



{{{y=(-12)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=3}}} Reduce.



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



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



{{{x=-4-3}}} Subtract {{{3}}} from both sides.



{{{x=-7}}} Combine like terms on the right side.



So the solutions are {{{x=-7}}} and {{{y=3}}}.



Which form the ordered pair *[Tex \LARGE \left(-7,3\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(-7,3\right)]. So this visually verifies our answer.



{{{drawing(500,500,-17,3,-7,13,
grid(1),
graph(500,500,-17,3,-7,13,-4-x,(-8+x)/(-5)),
circle(-7,3,0.05),
circle(-7,3,0.08),
circle(-7,3,0.10)
)}}} Graph of {{{x+y=-4}}} (red) and {{{-x-5y=-8}}} (green) 



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