Question

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

Answer 1

Answer:

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

Step-by-step 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.