Algebra Challenge: Solve the System -8x + 5y = 10 and -24x + 15y = 30

To solve this problem using the substitution method, we'll carefully examine the structure of the given system of equations:

• Given equations:
  1) $-8x + 5y = 10$
  2) $-24x + 15y = 30$

Notice that the second equation is exactly three times the first equation:

$-24x + 15y = 3(-8x + 5y) = 3 \times 10 = 30$

This implies the two equations are not independent; rather, they are multiples of each other.

This insight tells us that every solution of the first equation is also a solution of the second equation, which means:

The system has infinitely many solutions.

Given this conclusion, when examining the choices provided, the correct choice is "Infinite solutions."

Therefore, the solution to the system of equations is that it has infinite solutions.