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प्रश्न
Find the value of k for which each of the following system of equations has infinitely many solutions :
8x + 5y = 9
kx + 10y = 18
उत्तर
The given system of equation is
8x + 5y - 9 = 0
kx + 10y - 18 = 0
The system of equation is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where, `a_1 = 8, b_1 = 5, c_1 = -9`'
And `a_2 = k, b_2 = 10, c_2 = -18`
For a unique solution, we must have
`a_1/a_2 = b_1/b_2 = c_1/c_2`
`=>8/k = 5/10 = (-9)/(-18)`
Now
`8/k = 5/10`
`=> 8 xx 10 = 5 xx k`
`=> (8xx10)/5 = k`
`=> k = 8 xx 2 = 16`
Hence, the given system of equations will have infinitely many solutions, if k = 16
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