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Comparing the Ratios of Coefficients of a Linear Equation

For what valu...

Question

For what value of k the system of equations
5x + 2y = 2k , 2(k+1)x + ky = (3k +4)
Has an infinite solution ?

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Solution

a1/a2 = b1/b2 = c1/c2
System has infinitely many solutions, so
5/2(k+1) = 2/k = 2k/3k + 4
So, we get 5k = 4(k + 1)
5k = 4k + 4
k = 4

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Comparing the Ratios of Coefficients of a Linear Equation

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