To determine which of the given points are solutions to the inequality, we need to examine each point individually and test whether it satisfies the inequality.
The points to be checked are:
1. [tex]\((-2, -5)\)[/tex]
2. [tex]\((0, -4)\)[/tex]
3. [tex]\((1, 1)\)[/tex]
4. [tex]\((3, 5)\)[/tex]
5. [tex]\((5, 5)\)[/tex]
We are testing these points against the given inequality [tex]\(y < x\)[/tex].
1. Point [tex]\((-2, -5)\)[/tex]:
- x = -2
- y = -5
- Testing the inequality: [tex]\(-5 < -2\)[/tex]
- This is true because -5 is less than -2.
- Therefore, the point [tex]\((-2, -5)\)[/tex] satisfies the inequality.
2. Point [tex]\((0, -4)\)[/tex]:
- x = 0
- y = -4
- Testing the inequality: [tex]\(-4 < 0\)[/tex]
- This is true because -4 is less than 0.
- Therefore, the point [tex]\((0, -4)\)[/tex] satisfies the inequality.
3. Point [tex]\((1, 1)\)[/tex]:
- x = 1
- y = 1
- Testing the inequality: [tex]\(1 < 1\)[/tex]
- This is false because 1 is not less than 1.
- Therefore, the point [tex]\((1, 1)\)[/tex] does not satisfy the inequality.
4. Point [tex]\((3, 5)\)[/tex]:
- x = 3
- y = 5
- Testing the inequality: [tex]\(5 < 3\)[/tex]
- This is false because 5 is not less than 3.
- Therefore, the point [tex]\((3, 5)\)[/tex] does not satisfy the inequality.
5. Point [tex]\((5, 5)\)[/tex]:
- x = 5
- y = 5
- Testing the inequality: [tex]\(5 < 5\)[/tex]
- This is false because 5 is not less than 5.
- Therefore, the point [tex]\((5, 5)\)[/tex] does not satisfy the inequality.
After checking all points, the ones that satisfy the inequality [tex]\(y < x\)[/tex] are:
- [tex]\((-2, -5)\)[/tex]
- [tex]\((0, -4)\)[/tex]
Thus, the points that are solutions to the inequality are:
- [tex]\((-2, -5)\)[/tex] and [tex]\((0, -4)\)[/tex].
