y&=x^2+x-8\\y&=2x-2

If (x,y) is a solution to the system of equations above, what is the greatest possible value of \left|x-y\right| ?

A)
B)
C)
D)

 


 

Comments (2)

Sure. First, solve for x by substituting:

x^2+x-8=2x-2\\x^2-x-6=0\\(x-3)(x+2)=0

Now that you know x can equal 3 or -2, find the corresponding y-values by plugging back into the simpler equation:

y=2(3)-2=4
y=2(-2)-2=-6

So the two possible ordered pairs are (3, 4) and (-2, -6). The values of |x-y|, then, are:

|3-4|=1
|-2-(-6)|=4

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