Question

Which of the points on the graph is a solution for the simultaneous inequalities y is greater than 4x - 2 and y is greater than or equal to negative 1/3 x + 2 enter the x value followed by the y value

Answer 1

To find a point that satisfies both inequalities \( y > 4x - 2 \) and \( y \geq -\frac{1}{3}x + 2 \), we first need to analyze what each inequality represents graphically.

1. **For the inequality \( y > 4x - 2 \)**:
- The line \( y = 4x - 2 \) has a slope of 4 and a y-intercept at -2.
- The region above this line (not including the line itself) represents all the points that satisfy this inequality.

2. **For the inequality \( y \geq -\frac{1}{3}x + 2 \)**:
- The line \( y = -\frac{1}{3}x + 2 \) has a slope of -1/3 and a y-intercept at 2.
- The region on or above this line represents all points that satisfy this inequality.

Next, we need to find a point (x, y) that is in the region defined by both inequalities.

Let's evaluate some points.

### Test Point (0, 3):
- For \( y > 4x - 2 \):
\[
3 > 4(0) - 2 \quad \Rightarrow \quad 3 > -2 \quad \text{(True)}
\]
- For \( y \geq -\frac{1}{3}x + 2 \):
\[
3 \geq -\frac{1}{3}(0) + 2 \quad \Rightarrow \quad 3 \geq 2 \quad \text{(True)}
\]

Thus, the point (0, 3) satisfies both inequalities.

### Conclusion
A possible solution point (x, y) that satisfies both inequalities is:
\[
\boxed{0 \; 3}
\]