Question

Find the value of k for which the following pair of equations has no solution: + 2 = 3, ( − 1) + ( + 1) = ( + 2)

Answer 1

Answer:

Hope it helps

Step-by-step explanation:

These 2 simultaneous linear equations will have no solutions if, 

A / a = B / b 

i.e., the ratio of the x-coefficients is equal to the ratio of y-coefficients. 

x + 2y = 3(k-1)x+(k+1)y = k+2 

First equation: x + 2y = k + 2 

Or, 1x + 2y - (k+2) = 0 [A = 1, B = 2, C = -(k+2)] 

Second equation: 3(k-1)x+(k+1)y = k+2 

Or, (3k-3)x + (k+1)y - (k+2) = 0 [a = 3k-3, b = k+1, c = -(k+2)] 

Required condition: 

A / a = B / b 

Or, 1 / (3k-3) = 2 / (k+1) 

Or, 2 (3k-3) = 1 (k+1) [By cross-multiplication] 

Or, 6k - 6 = k + 1 

Or, 6k - k = 1 + 6 

Or, 5k = 7 

k = 5/7

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