Question

For what value of k will the following linear system have infinitely many solutions?

2a+b=-6, 6a+kb=-18

Answers

  1. There are infinitely many solutions to a linear equation with the same variable term on both sides of the equation.
    We have to find the coefficient of “b”
    from first equation:
    • 2a + b = -6
    • b = -6 – 2a
    from second equation:
    • 6a + kb = -18
    • b = (-18 – 6a)/k
    solve them simultaneously:
    • (-18 – 6a)/k = -6 – 2a
    • (-18 – 6a)/(-6 – 2a) = k
    • k = 3

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