Question

The linear combination method is applied to a system of equations: (4x + 10y = 12) (10x + 25y = 30) – 2x + 5y = 6 –2x – 5y = –6 0 = 0 What does 0 = 0 indicate about the solutions of the system? There are 0 solutions to the system. The solution to the system is (0, 0). There are solutions to the system at the x- and y-intercepts. There are infinitely many solutions to the system.

Answer 1

The answer is D. There are infinitely many solutions to the system. I got it right.

Answer 2

We are given system of equations :  (4x + 10y = 12) (10x + 25y = 30).

On solving system of equations, we are getting 0=0.

Please see, we are getting left side equal to right side.

When we get left side equal to right side on solving system of equations it would show that, it would true for all x values for both equation.

Means the system of equation would have infinitely many solution.

Therefore, correct option is :

There are infinitely many solutions to the system.