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Question

For what value of k, the equations 5x-2y+8=0 & 15x+ky=-24 have an unique solution ?


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Solution

Step 1: Estimate the constants of the equations

The given equations are,

5x-2y+8=0

15x+ky=-24

The equations are of the form a1x+b1y+c1=0 and a2x+b2y+c2=0

Here, a1=5,b1=-2,c1=8

a2=15,b2=k,c2=24

Step 2: Calculate the value of k

Here, a1a2b1b2 i.e., the given system of equations has a unique solution.

515-2k

5k-30

k-305

k-6

Thus, k can have any real value except -6.


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