For what value of the constant a,

\(\begin{align*} 2x + 5y &= -8,\\ 6x &= 16 + a - 15y \end{align*}\)

does the system of equations below have infinitely many solutions?

Guest May 31, 2019

#1**+3 **

2x + 5y = -8 Multiply both sides of this equation by 3.

6x + 15y = -24

6x = 16 + a - 15y Add 15y to both sides of this equation.

6x + 15y = 16 + a

So now our two equations are:

6x + 15y = -24

6x + 15y = 16 + a

The system will have infinitely many solutions when both equations are identical.

So the system will have infinitely many solutions when....

-24 = 16 + a Subtract 16 from both sides of this equation.

-40 = a

a = -40

hectictar May 31, 2019