Question

Which point plotted on the grid represents a solution to the system of inequalities graphed?

y>−2x+3
𝑦
>
−
2
𝑥
+
3


y<3x−3
𝑦
<
3
𝑥
−
3


(1 point)
The point (,) represents a solution to the system.

Answer 1

To determine which point represents a solution to the system of inequalities given:

1. \( y > -2x + 3 \)
2. \( y < 3x - 3 \)

you'll need to find a point that satisfies both inequalities.

### Steps to Check for Solutions:

1. **Check the first inequality \( y > -2x + 3 \)**:

- Choose a point (x, y) and plug in the values to see if it makes the inequality true.

2. **Check the second inequality \( y < 3x - 3 \)**:

- Similarly, plug in the (x, y) values into this inequality.

### Example Points:

Let's say we check the point \( (0, 5) \):

1. For \( y > -2x + 3 \):

- Plug in \( x = 0 \) and \( y = 5 \):
- \( 5 > -2(0) + 3 \) -> \( 5 > 3 \) (True)

2. For \( y < 3x - 3 \):

- Plug in \( x = 0 \) and \( y = 5 \):
- \( 5 < 3(0) - 3 \) -> \( 5 < -3 \) (False)

So, \( (0, 5) \) is **not** a solution.

### Try another point \( (1, 1) \):

1. For \( y > -2x + 3 \):

- \( 1 > -2(1) + 3 \) -> \( 1 > 1 \) (False)

### Let's test \( (0, 4) \):

1. For \( y > -2x + 3 \):

- \( 4 > -2(0) + 3 \) -> \( 4 > 3 \) (True)

2. For \( y < 3x - 3 \):

- \( 4 < 3(0) - 3 \) -> \( 4 < -3 \) (False)

### In summary:

You would need to check various points until you find one that satisfies both inequalities.

If you have a specific point (x, y) in mind, check it against both inequalities and see if it meets both conditions. If you want help checking a specific point, please provide it!