SOLUTION: Sketch the graphs of y=x^2-4x+3 and x-2y=-6 on the same set of axes. Find the coordinates of each intersection point.

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Question 314411: Sketch the graphs of y=x^2-4x+3 and x-2y=-6 on the same set of axes. Find the coordinates of each intersection point.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Sketch the graphs of y=x^2-4x+3 and x-2y=-6 on the same set of axes. Find the coordinates of each intersection point.

Solve the system:

system%28y=x%5E2-4x%2B3%2Cx-2y=-6%29

Substitute %28x%5E2-4x%2B3%29 for y in the second equation:

x-2y=-6%29
x-2%28x%5E2-4x%2B3%29=-6%29
x-2x%5E2%2B8x-6=-6%29
-2x%5E2%2B9x-6=-6%29
-2x%5E2%2B9x=0%29
x%28-2x%2B9%29=0

Set each factor = 0

x=0  -2x+9=0
       -2x=-9
         x=4.5

Find the y-value that goes with x=0 by
substituting 0 for x in

x-2y=-6%29
0-2y=-6%29
-2y=-6%29
y=3%29

So one point of intersection is (x,y) = (0,3)

Find the y-value that goes with x=4.5 by
substituting 4.5 for x in

x-2y=-6%29
4.5-2y=-6%29
-2y=-10.5%29
y=5.25%29

So the other point of intersection is (x,y) = (4.5,5.25)        



Edwin