Question

the system of equations is solved using the linear combination method.\\(\frac{1}{2}x + 4y = 8\\) \\( \to -2left(\frac{1}{2}x + 4y = 8
ight) \\) \\( \to -x - 8y = -16\\)\\(3x + 24y = 12\\) \\( \to \frac{1}{3}(3x + 24y = 12) \\) \\( \to x + 8y = 4\\)\\(\frac{0=-12}{}\\)\\(\\)what does \\(0 = -12\\) mean regarding the solution to the system?\\(\\)\\(\circ\\) there are no solutions to the system because the equations represent parallel lines.\\(\\)\\(\circ\\) there are no solutions to the system because the equations represent the same line.\\(\\)\\(\circ\\) there are infinitely many solutions to the system because the equations represent parallel lines.\\(\\)\\(\circ\\) there are infinitely many solutions to the system because the equations represent the same line

Explanation:

When solving a system of linear equations, if you end up with a false statement like $0=-12$, this means the two equations represent parallel, non-intersecting lines. Parallel lines never cross, so there are no points that satisfy both equations at the same time. The option claiming the equations are the same line is incorrect because identical lines would result in a true statement like $0=0$, not a false one.

Answer:

There are no solutions to the system because the equations represent parallel lines.