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

To find the point that is not a solution to the system of linear inequalities, we need to check each point and see if it satisfies both inequalities. None of the given points would not be a solution to the system of linear inequalities.

Step-by-step explanation:

To find the point that is not a solution to the system of linear inequalities, we need to check each point and see if it satisfies both inequalities. The system of inequalities is: y ≥ x + 5 and y ≥ (2/3)x + 6. Let's check each point:

• Point (12, 7): Checking the first inequality, 7 ≥ 12 + 5 is true. Checking the second inequality, 7 ≥ (2/3) * 12 + 6 is also true. So (12, 7) satisfies both inequalities.
• Point (-12, 1): Checking the first inequality, 1 ≥ -12 + 5 is true. Checking the second inequality, 1 ≥ (2/3) * -12 + 6 is also true. So (-12, 1) satisfies both inequalities.
• Point (-12, 9): Checking the first inequality, 9 ≥ -12 + 5 is true. Checking the second inequality, 9 ≥ (2/3) * -12 + 6 is also true. So (-12, 9) satisfies both inequalities.
• Point (-12, 6): Checking the first inequality, 6 ≥ -12 + 5 is true. Checking the second inequality, 6 ≥ (2/3) * -12 + 6 is true as well. So (-12, 6) satisfies both inequalities.

Therefore, none of the given points (12, 7), (-12, 1), (-12, 9), and (-12, 6) would not be a solution to the system of linear inequalities.