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Is (8,2)(8,\,2) a solution to this system of inequalities?\newlinex+y10x + y \geq 10\newline17x+11y217x + 11y \leq 2\newlineChoices:\newline(A)yes\newline(B)no

Full solution

Q. Is (8,2)(8,\,2) a solution to this system of inequalities?\newlinex+y10x + y \geq 10\newline17x+11y217x + 11y \leq 2\newlineChoices:\newline(A)yes\newline(B)no
  1. Check Point (8,2)(8, 2): Check if the point (8,2)(8, 2) satisfies the inequality x+y10x + y \geq 10. Substitute x=8x = 8 and y=2y = 2 into the inequality. 8+2108 + 2 \geq 10 101010 \geq 10 Since 1010 is equal to 1010, the inequality holds true.
  2. Check Inequality 11: Check if the point (8,2)(8, 2) satisfies the inequality 17x+11y217x + 11y \leq 2. Substitute x=8x = 8 and y=2y = 2 into the inequality. 17(8)+11(2)217(8) + 11(2) \leq 2 136+222136 + 22 \leq 2 1582158 \leq 2 Since 158158 is not less than or equal to 22, the inequality does not hold true.
  3. Check Inequality 22: Determine if the point (8,2)(8, 2) is a solution to the system of inequalities.\newlineSince the point (8,2)(8, 2) satisfies the first inequality but does not satisfy the second inequality, it is not a solution to the system of inequalities.

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