Which of the following points (x, y, z) is in the solution set of the system of inequalities: x + 3y − z ≤ 5 x − 2z ≥ 0 x + y + z ≤ 10 (a) (1, 1, 3) (b) (2, 2, 1) (c) (6, −2, 2) (d) (8, 3, 1) (e) (−1, 8, −2) (f) None of these please explain as well :) Thank you

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Which of the following points (x, y, z) is in the solution set of the system of inequalities: x + 3y − z ≤ 5 x − 2z ≥ 0 x + y + z ≤ 10 (a) (1, 1, 3) (b) (2, 2, 1) (c) (6, −2, 2) (d) (8, 3, 1) (e) (−1, 8, −2) (f) None of these please explain as well :) Thank you

Mathematics
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you could enter in the choices and see which satisfies the inequalities
so (c) is correct answer?
let's check (6,-2,2) x=6 y=-2 z=2 \[6+3(-2)-2 \le 5 \\ 6-6-2 \le 5 \\ -2 \le 5 \text{ the first inequality is true } -2 \text{ is less than } 5 \\ 6-2(2) \ge 0 \\ 6-4 \ge 0 \\ 2 \ge 0 \text{ the second inequality is true 2 is greater than 0 } \\ 6-2+2 \le 10 \\ 6 \le 10 \text{ the third inequality is true 6 is less than 10 }\] so yes (6,-2,2) seems to check out

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can there be more than one option?
I think that's the only one..
checking (1,1,3) \[1+3-3 \le 5 \\1 \le 5 \text{ first inequality true }\] \[1-2(3) \ge 0 \\ 1-6 \ge 0 \\ -5 \ge 0 \text{ \not true }\] no need to check third inequality (1,1,3) is not a solution checking (2,2,1) \[2+6-1 \le 5 \text{ is false }\] no need to check the other inequalities (2,2,1) is not a solution checking (8,3,1) \[8+9-1 \le 5 \text{ is false } \\ (8,3,1) \text{ doesn't work }\] checking (-1,8,-2) \[-1+3(8)+2 \le 5 \text{ is false } \\ (-1,8,-2) \text{ is \not a solution }\] most of those choices fail at the first inequality
good job
Thank you :)

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