Question 324855


Start with the given system of equations:

{{{system(-4x+2y=10,-4x-2y=6)}}}



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



{{{(-4x+2y)+(-4x-2y)=(10)+(6)}}}



{{{(-4x+-4x)+(2y+-2y)=10+6}}} Group like terms.



{{{-8x+0y=16}}} Combine like terms.



{{{-8x=16}}} Simplify.



{{{x=(16)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{x}}}.



{{{x=-2}}} Reduce.



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{{{-4x+2y=10}}} Now go back to the first equation.



{{{-4(-2)+2y=10}}} Plug in {{{x=-2}}}.



{{{8+2y=10}}} Multiply.



{{{2y=10-8}}} Subtract {{{8}}} from both sides.



{{{2y=2}}} Combine like terms on the right side.



{{{y=(2)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



{{{y=1}}} Reduce.



So the solutions are {{{x=-2}}} and {{{y=1}}}.



Which form the ordered pair *[Tex \LARGE \left(-2,1\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(-2,1\right)]. So this visually verifies our answer.



{{{drawing(500,500,-12,8,-9,11,
grid(1),
graph(500,500,-12,8,-9,11,(10+4x)/(2),(6+4x)/(-2)),
circle(-2,1,0.05),
circle(-2,1,0.08),
circle(-2,1,0.10)
)}}} Graph of {{{-4x+2y=10}}} (red) and {{{-4x-2y=6}}} (green)