Which graph represents the solution to the system of inequalities? x + y ≤ 50 x ≥ 20
1 answer:
Consider the inequality x+y≤50, that is y≤-x+50
we first draw the line y=-x+50, using the x and y intercepts:
(50, 0) and (0, 50). To check which region to color, we pick any point, for example (0, 25). for this point the inequality 25≤-0+50 is true, so we have picked a point in the region that we will color. (we color it with yellow as shown in the picture)
consider <span>x ≥ 20. This inequality represents all vertical lines starting at x=20, and to the right of this line. So we color the region to the right of x=20. (colored with light gray)
The solution of the inequality system is the intersection of both regions, that is the region which is colored with both colors.
Solution: the purple region</span>
we first draw the line y=-x+50, using the x and y intercepts:
(50, 0) and (0, 50). To check which region to color, we pick any point, for example (0, 25). for this point the inequality 25≤-0+50 is true, so we have picked a point in the region that we will color. (we color it with yellow as shown in the picture)
consider <span>x ≥ 20. This inequality represents all vertical lines starting at x=20, and to the right of this line. So we color the region to the right of x=20. (colored with light gray)
The solution of the inequality system is the intersection of both regions, that is the region which is colored with both colors.
Solution: the purple region</span>
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