which graph shows the solution to the system of linear inequalities? y≥2x + 1 y≤2x - 2
which graph shows the solution to the system of linear inequalities? y≥2x + 1 y≤2x - 2
Answer
Explanation:
Step1: Analyze first inequality
The line (y = 2x+1) has a slope of 2 and y - intercept of 1. The inequality (y\geq2x + 1) means the region above the line (y = 2x+1) (including the line itself since it is (\geq)).
Step2: Analyze second inequality
The line (y=2x - 2) has a slope of 2 and y - intercept of - 2. The inequality (y\leq2x - 2) means the region below the line (y = 2x-2) (including the line itself since it is (\leq)).
Step3: Check for intersection
Since the two lines (y = 2x+1) and (y = 2x - 2) have the same slope (m = 2), they are parallel. And (1>-2), so the region above (y = 2x + 1) and the region below (y = 2x-2) do not intersect. There is no solution to the system of inequalities.
Answer:
There is no solution to the given system of linear inequalities as the regions defined by (y\geq2x + 1) and (y\leq2x - 2) (where the lines are parallel) do not overlap.