Question

The sum of two numbers is at least 5, and the sum of one of the numbers, x, and 5 times the second number, y, is no more than 15. Enter the system of inequalities that represents the situation. Then select the graph of the system and select one possible solution.

Answer 1

• The system of inequalities are x+y≥5 and x+5y≤15

,

• 4 and 2

Explanation:

As given in the question:

• The first number = x

,

• The second number = y

The sum of the two numbers is at least 5. We can represent this using the inequality:

`x+y\ge5`

The sum of one of the numbers, x, and 5 times the second number, y, is no more than 15.

`x+5y\le15`

The system of inequalities are x+y≥5 and x+5y≤15.

The inequalities are graphed below:

The correct graph is Option C.

A possible solution to the system of inequalities is 4 and 2.

Every other point is outside the region that satisfies the two inequalities.