Question

For what values of k is the system of equations `3x -2 (k-1)y =30 and 4x -2y = 35` consistent.

Answer 1

Consider the equations `a_1x + b_1y + c_1=0 and a_2x +b_2y +c_2=0`. If this pair of equation is consistent, `(a_1)/(a_2) ne (b_1)/(b_2)`.
For the above equations let `a_1 = 3, b_1=-2(k-1), a_2 =4 and b_2 =-2`.
Now, `(3)/(4) ne (-2(k-1))/(-2)`
`rArr 4(k-1) ne 3 rArr k ne 7//4`
For all values of `k`, except `7//4`, the pair of equations is consistent.