Question

Which of the following is a solution to the system of inequalities shown below?5x+2y>19x+y≥5(1 point)Responses(0,1)open paren 0 comma 1 close paren(5,5)open paren 5 comma 5 close paren(0,0)open paren 0 comma 0 close paren(5,−1)

Answer 1

To determine which of the given points is a solution to the system of inequalities:

1. **First inequality**: \(5x + 2y > 19\)
2. **Second inequality**: \(x + y \geq 5\)

We will check each point to see if it satisfies both inequalities.

**Point (0, 1)**:
- For \(5x + 2y > 19\): \(5(0) + 2(1) = 0 + 2 = 2\) (not greater than 19)
- For \(x + y \geq 5\): \(0 + 1 = 1\) (not greater than or equal to 5)

**Point (5, 5)**:
- For \(5x + 2y > 19\): \(5(5) + 2(5) = 25 + 10 = 35\) (greater than 19)
- For \(x + y \geq 5\): \(5 + 5 = 10\) (greater than or equal to 5)

**Point (0, 0)**:
- For \(5x + 2y > 19\): \(5(0) + 2(0) = 0\) (not greater than 19)
- For \(x + y \geq 5\): \(0 + 0 = 0\) (not greater than or equal to 5)

**Point (5, -1)**:
- For \(5x + 2y > 19\): \(5(5) + 2(-1) = 25 - 2 = 23\) (greater than 19)
- For \(x + y \geq 5\): \(5 + (-1) = 4\) (not greater than or equal to 5)

After checking all points, the only point that satisfies both inequalities is:

\((5, 5)\)

So, the correct response is \((5, 5)\).