For what value of the constant $a$ does the system of equations below have infinitely many solutions?\begin{align*} 2x + 5y &= -8,\\ 6x &= 16 + a - 15y \end{align*}

Guest Jul 9, 2022

#1**0 **

In order for a system to have infinitely many solutions, the equations must represent the same coefficients and constants.

We have the equations:

2x + 5y = - 8

6x + 15y = 16 + a

Multiplying the first equation by 3 gives us:

6x + 15y = -24

6x + 15y = 16 + a

In order for this system to have infintely many solutions, 16 + a = -24

This gives us -40 for a.

Voldemort Jul 9, 2022