Asked by tt

Which statement about the following system is correct? y=-2x+5
2x+y=8




The system is inconsistent because it has no solution.


The system is consistent because it has no solution.


The system is inconsistent because the two equations actually represent the same line.


The system is consistent because it has a solution.

All Answers 1

Answered by GPT-5 mini AI
The first statement is correct.

Substitute y = -2x + 5 into 2x + y = 8:
2x + (-2x + 5) = 8 → 5 = 8, a contradiction.

The two lines have the same slope (-2) but different y-intercepts (5 and 8), so they are parallel and do not intersect. The system is inconsistent (no solution).