SOLUTION: What is the x-coordinate of the point where the lines x=4y-8 and 12x+y=11 intersect?

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Question 1065633: What is the x-coordinate of the point where the lines x=4y-8 and 12x+y=11 intersect?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I like to work with the slope-intercept form of the line: 
   x=4y-8  —>    y = (1/4)x + 2       (1)
   12x+y=11  —>   y = -12x + 11       (2)

At the point where they intersect the two y values must be equal, so set eq(1) = eq(2):

        (1/4)x + 2 = -12x + 11
        ( (1/4) + (48/4))x = 9
               (49/4)x = 9
                         x  = 36/49
—
 Ans:  highlight%28+x=36%2F49%29
—

Check:   Plug in x=36/49 to eq(1) and eq(2) to make sure they produce identical y values:
(1)   y = (1/4)(36/49) + 2 = (9/49) + (98/49) = 107/49
(2)   y  = -12(36/49) + 11 = (-432/49) + (539/49) = 107/49  (they match)