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The solutions to the system of inequalities will be in the region where the shaded areas overlap . Notice that (2, 3), (3 , 4), and (4, 0) are all in the overlap.
“But what about (1, 2)? That’s kind of in the overlap too.”
Notice that the graph of the line y > – x + 3, where the point (1, 2) rests, is dashed (as opposed to the graph of the line for y ≤ 3 x , which is solid). Since the boundary is a dashed line, the line itself is not included in the solution set. Therefore, (1, 2) does not satisfy the inequality y > – x + 3: 2>−1+3 2>2 > → Shade above the line < → Shade below the line
➢ Practice
Which of the following graphs in the xy -plane, where point O is the origin, could represent the inequality 𝑝𝑥 + 𝑞𝑦 ≤ 𝑟 , where 0 < 𝑝 < 𝑞 < 𝑟 ? Assume all of the graphs are the same scale.
(C)
(D)
(A)
(B)
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