Answer:
A, C, D, H*, K
Step-by-step explanation:
Given:
y ≤ -2x +10
y > x -2
Find:
Points on the graph that satisfy the system of inequalities.
Solution:
In the attachment, we have plotted the boundary lines on the graph and indicated the half-plane that is part of the solution set. The points that satisfy both inequalities are ...
A, C, D, H*, K
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Since the relations are written in slope-intercept form, it is convenient to plot the lines starting with the y-intercept, and working from there using the "rise"/"run" of the slope. The first inequality has a slope of -2, so the line falls two grid spaces for each one it goes to the right. y-values are less than or equal to those on the line, so shading is below the line.
The second inequality has a slope of +1, so the line rises 1 grid space for each one i goes to the right. y-values are greater than those on the line, so shading is above the line.
The points in the solution space are those to the left of the crossing point of the lines.
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* Comment on the question
The inequalities used in this answer were not supplied with this question, but were part of comments added to the question. The second inequality in your previous post was y > 1/2x -2. The shallower slope of that boundary line will exclude point H from the solution set. (H is on the boundary line, which is not part of the solution.)
