Seudónimo Seudónimo
  • 18-04-2022
  • Mathematics
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For what value of k will the following linear system have infinitely many solutions?

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

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fieryanswererft
fieryanswererft fieryanswererft
  • 18-04-2022

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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