Question

Which point would not be a solution to the system of linear inequalities shown below? y\ge x+5\hspace{50px}y\ge\frac{2}{3} x+6 y≥x+5y≥ 3 2 ​ x+6 (12, 7) (-12, 1) (-12, 9) (-12, 6)

Answer 1

Answer:

(12,7) is not a solution

Step-by-step explanation:

Given

$y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6$

Required

Point that is not a solution

We have:

$y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6$

Substitute $\frac{2}{3}x + 6$ for y in the first inequality

$\frac{2}{3}x + 6 \ge x + 5$

Collect like terms

$\frac{2}{3}x - x \ge 5-6$

$-\frac{1}{3}x \ge -1$

Solve for x (the inequality will change because we are to divide by a  negative number_

$x \le -1/-\frac{1}{3}$

$x \le 3$

Without solving further, we can conclude that the first option is not a solution.

Because (12,7) implies that $x =12$

Compare $x =12$ to $x \le 3$, then $x \le 3$ is false