Question 150380

Start with the given system of equations:



{{{system(y=2x,x-y=4)}}}



{{{x-y=4}}} Start with the second equation.



{{{x-2x=4}}} Plug in {{{y=2x}}}



{{{-x=4}}} Combine like terms on the left side.



{{{x=(4)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.



{{{x=-4}}} Reduce.



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Since we know that {{{x=-4}}}, we can use this to find {{{y}}}.



{{{y=2x}}} Go back to the first equation.



{{{y=2(-4)}}} Plug in {{{x=-4}}}.



{{{y=-8}}} Evaluate the right side.



So the answer is {{{x=-4}}} and {{{y=-8}}}.



This means that the system is consistent and independent.



Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(-4,-8\right)]. So this visually verifies our answer.



{{{drawing(500,500,-14,6,-10,10,
grid(1),
graph(500,500,-14,6,-10,10,2x,(4-x)/(-1)),
circle(-4,-8,0.05),
circle(-4,-8,0.08),
circle(-4,-8,0.10)
)}}} Graph of {{{y=2x}}} (red) and {{{x-y=4}}} (green)