Answer:
(b) and (c)
Step-by-step explanation:
When the equation of a line is given in slope-intercept form ([tex]y=mx+b[/tex]), m represents the slope of the line and b represents the y-intercept. As we can see, the two lines given have the same slope (-3), but different y-intercepts (the first line has a y-intercept of 4 and the second line has a y-intercept of -11).
Since the slopes of the two lines are the same, they will be parallel, and since their y-intercepts are different, they will not be the same line. Therefore, the two lines will not intersect (a solution to the system is any point where the two lines do intersect), and there is no solution to the system.
As a general rule:
- If two lines have different slopes, there will be exactly one solution to the system (the lines will not be parallel and will intersect at exactly one place)
- If two lines have the same slope, and the same y-intercept, there will be infinitely many solutions (the two lines will be the same, and any point on the line will be a solution)
- If two lines have the same slope, but different y-intercepts, they will be parallel and will never intersect, so there will be no solution.
