SOLUTION: if the straight line L1: 3x+y-9=0 and L2: 2x-9y+k=o have the same x-intercept, find (a) the value of k (b) the y-intercept

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Question 935881: if the straight line L1: 3x+y-9=0 and L2: 2x-9y+k=o have the same x-intercept, find
(a) the value of k
(b) the y-intercept
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
first equation is 3x + y - 9 = 0
second equation is 2x + 9y - k = 0

solve for y in both equations.

you get:

first equation becomes y = -3x + 9
second equation becomes y = (-2x+k)/9

the x-intercept occurs when the value of y is equal to 0.

set both equations equal to 0 to get:

first equation becomes -3x + 9 = 0
second equation becomes (-2x+i)/9 = 0

solve for x in the first equation to get x = 3
solve for x in the second equation to get 2x = k

when y = 0, the value of x in both equations must be the same since both equations have the same x-intercept, so the second equation becomes 2(3) = k.

solve for k in the second equation to get k = 6.

both equations will have the same x-intercept when k = 6.

when k = 6, the second equation becomes y = (-2x + 6) / 9

the equations are now:

first equation is y = -3x + 9
second equation is y = (-2x + 6)/9

the y-intercept is the value of y when x is equal to 0.

replace x with 0 in both equations to get:

first equation becomes y = 9
second equation becomes y = 2/3.

the y-intercept for the first equation is 9.
the y intercept for the second equation is y = 2/3.

the graph of both equations is shown below:

i placed 2 horizontal lines at y = 9 and y = 2/3, so you can see the y-intercepts better.

the line that crosses the y-axis at y = 2/3 is the second equation.
the line that crosses the y-axis at y = 9 is the first equation.

the equation of the lowest horizontal line is y = 2/3.
the equation of the highest horizontal line is y = 9.