For what value of the constant a does the system of equations below have infinitely many solutions?
2x + 5y = -8
6x = 16 + a - 15y + 4x + 10y
Solve with substitution:
2x = -8 - 5y
\(x = -4 - \frac{5}{2}y\)
Substitute x into the second equation:
\(6(-4-\frac{5}{2}y) = 16+a-15y+4(-4-\frac{5}{2}y) +10y\)
\(\rightarrow -24-15y=16+a-15y-16-10y+10y\)
Simplify:
-24 = a
So, for the system to have infinite solutions, a = -24.
