Question

For which system of inequalities is (3,-7) a solution? A. x + y < -4 3x + 2y < -5 B. x + y ≤ -4 3x + 2y < -5 C. x + y < -4 3x + 2y ≤ -5 D. x + y ≤ -4 3x + 2y ≤ -5

Answer 1

The correct option is;

D x + y ≤ -4, 3·x + 2·y ≤-5

Explanation:

A. For the system of inequality, x + y < -4, 3·x + 2·y <-5

We have;

y < -4 - x, When x = 3, y < -7

y < -2.5 - 1.5·x, When x = 3, y = -7

B. For the system of inequality, x + y ≤ -4, 3·x + 2·y <-5

We have;

y ≤ -4 - x, When x = 3, y ≤ -7

y < -2.5 - 1.5·x, When x = 3, y < -7

C. For the system of inequality, x + y < -4, 3·x + 2·y ≤-5

We have;

y < -4 - x, When x = 3, y < -7

y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7

D. For the system of inequality, x + y ≤ -4, 3·x + 2·y ≤-5

We have;

y ≤ -4 - x, When x = 3, y ≤ -7

y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7

Therefore, the system of inequality for which (3, -7) is a solution is D, x + y ≤ -4, 3·x + 2·y ≤-5.