Question

texascollegebridgedy paths > tx math bridge - stage 2graphing systems of lineartopic test:topic: graphing systems of linear equationsprogress:the movement of the progress may not be even because questions can be worth more or less (including zero) depending on your answer.which statement about the following system is correct?$y = -2x + 5$$2x + y = -5$○ the system is consistent because it has no solution.○ the system is consistent because it has a solution.○ the system is inconsistent because it has no solution.○ the system is inconsistent because the two equations actually represent the same line.

Explanation:

Step1: Rewrite second equation

Rearrange $2x + y = -5$ to slope-intercept form:
$y = -2x -5$

Step2: Compare slopes and intercepts

First equation: $y = -2x +5$ (slope $m=-2$, y-intercept $b=5$)
Second equation: $y = -2x -5$ (slope $m=-2$, y-intercept $b=-5$)

Step3: Analyze system consistency

Equal slopes, different intercepts mean parallel lines, no solution. Inconsistent systems have no solutions.

Answer:

The system is inconsistent because it has no solution.