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.

Since combining the equations will result to 0 = -12, it means that there are: A. no solutions to the system because the linear equations represent parallel lines.

Equations of Parallel Lines

A linear equation, where m is the slope and b is the y-intercept, can be represented as y = mx + b.
The slope of two lines that are parallel to each other is always the same.
Solution of two linear equations is the point where the line of the two linear equations intersect.

Therefore, since the system of linear equations given have the same slope, the lines of both equations are parallel and cannot intersect.

Thus, since combining the equations will result to 0 = -12, it means that there are: A. no solutions to the system because the linear equations represent parallel lines.

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