Question

Is x = -4 and y = 3 a solution of the following inequalities?

-10x - 3y < -6
O Solution
O Not a solution
-10x – 3y = –6
O Solution
O Not a solution
-10x - 3y > -6
O Solution
O Not a solution
-10x – 3y - 6
O Solution
O Not a solution

Answer 1

After substituting x = -4 and y = 3 into each statement, only the third inequality (-10x - 3y > -6) is satisfied; the first two are not. The last expression is incomplete without a relational operator.

Step-by-step explanation:

To determine if x = -4 and y = 3 is a solution for the given inequalities, we need to substitute the values into each inequality and check the truthfulness of each statement.

1. For the inequality -10x - 3y < -6, substituting x and y gives:
   -10(-4) - 3(3) = 40 - 9 = 31, which is not less than -6. Therefore, it is not a solution.
2. For the equation -10x - 3y = -6, substituting x and y gives: -10(-4) - 3(3) = 31, which is not equal to -6. Therefore, it is not a solution.
3. For the inequality -10x - 3y > -6, substituting x and y gives: -10(-4) - 3(3) = 31, which is greater than -6. Therefore, it is a solution.
4. For the expression -10x - 3y - 6, it's unclear whether this is an inequality or equation, and we lack a relational operator (like <, >, or =) to make a definitive conclusion.

Hence, only the third case satisfies the condition with the given x and y.