Find the value of K for which the following pair of linear equations has no solution: K x + 2y = K – 2 ; 8 x + K y = K
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Answer:
kx + 2y = k - 2
8x + ky = k
The system of equations has no solutions if the lines are parallel, thus:
2y = -kx + k - 2
y = (-k/2)x + (k - 2)/2
ky = -8x + k
y = (-8/k)x + 1
-k/2 = -8/k
k^2 = 16
k = ±4
Also:
(k - 2)/2 ≠ 1
k - 2 ≠ 2
k ≠ 4
k can not be +4 thus the only value for k is -4:
k = -4
Let’s check the results:
y = (-k/2)x + (k - 2)/2
y = 2x + 2 => first equation in slope-intercept form
y = (-8/k)x + 1
y = 2x + 1 => 2nd equation in slope-intercept form
The lines are parallel therefore no solution to the system.
Step-by-step explanation:
hope it helps you good day!!
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