Math

QuestionFind the values of hh and kk where (12,h)(12, h) is the intersection of x+4y=20x + 4y = 20 and 2x+ky18=02x + ky - 18 = 0.

Studdy Solution

STEP 1

Assumptions1. The point of intersection of the two lines is given by the coordinates (12,h)(12, h). . The equations of the two lines are x+4y=20x+4y=20 and x+ky18=0x+ky-18=0.
3. We need to find the values of hh and kk.

STEP 2

First, we can substitute the x-coordinate of the point of intersection into the first equation to solve for hh.
x+4y=20x+4y=20Substitute x=12x=12 into the equation.
12+4h=2012+4h=20

STEP 3

Now, solve for hh.
h=2012h=20-12h=8h=8h=8/h=8/h=2h=2

STEP 4

Now that we have found hh, we can substitute the coordinates of the point of intersection into the second equation to solve for kk.
2x+ky18=02x+ky-18=0Substitute x=12x=12 and y=2y=2 into the equation.
212+k218=02*12+k*2-18=0

STEP 5

implify the equation and solve for kk.
24+2k18=024+2k-18=02k=18242k=18-242k=2k=-k=/2k=-/2k=3k=-3The values of hh and kk are2 and -3, respectively.

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