Question

For what values of h and k does the linear system have infinitely many solutions? 2x1 + 5x2 = −1 hx1 + kx2 = 7

Answer 1

The values of
`h` and
`k` for a linear system with infinitely many solutions are -2 and 5, respectively.

Explanation:

Let
`2\cdot x_(1)+5\cdot x_(2) = -1\cdot h\cdot x_(1) + k\cdot x_(2) = 7`, if this linear system has infinitely many solutions, then the following conditions must be met:

`-1\cdot h = 2` and
`k = 5`.

`h = -2` and
`k = 5`

The values of
`h` and
`k` for a linear system with infinitely many solutions are -2 and 5, respectively.