Question

The system of equations is solved using the linear combination method.

StartLayout 1st row 1st column one-half x + 4 y = 8 right-arrow 2nd column negative 2 (one-half x + 4 y = 8) right-arrow 3rd column negative x minus 8 y = negative 16 2nd row 1st column 3 x + 24 y = 12 right-arrow 2nd column one-third (3 x + 24 y = 12) right arrow x + 8 y = 4 with Bar Underscript 3rd row 3rd column 0 = negative 12 EndLayout

What does 0 = −12 mean regarding the solution to the system?

There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.

Answer 1

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

Explanation: 0 = −12 is a contradiction, so the system is inconsistent. The two equations have the same slope (−1/8) but different intercepts, so they are distinct parallel lines.