For some constant real numbers p, k and a, consider the following system of linear equations in x and y:
px - 4y = 2
3x + ky= a
A necessary condition for the system to have no solution for (x, y ), is
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Explanatory Answer
A necessary condition for the system to have no solution for (𝑥,𝑦), is
The condition is a1a2=b1b2≠c1c2
i.e., p3=−4k≠2a
For p3=−4k;pk+12=0
For −4k≠2a;−4a≠2k⇒2a+k≠0
For p3≠2a;pa−6≠0
The question is "For some constant real numbers p,k and a, consider the following system of linear equations in x and y :
A necessary condition for the system to have no solution for (x,y), is "
Hence, the answer is '2a+k≠0'
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