Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set: y < -4/5 x + 7 and y > 2x - 7.

Steps to Solve

1. Identify the inequalities

First, we need to identify the two inequalities. Let's say the inequalities are:

• $y < 2x + 1$
• $y \geq -x + 3$

2. Rewrite the inequalities as equations

Next, we can rewrite the inequalities as equations to find the boundary lines:

• For $y < 2x + 1$, the corresponding equation is $y = 2x + 1$.
• For $y \geq -x + 3$, the corresponding equation is $y = -x + 3$.

3. Graph the lines

Now we graph the lines on a coordinate plane:

• For the line $y = 2x + 1$, plot the y-intercept (0, 1) and use the slope (2) to find another point, like (1, 3).
• For the line $y = -x + 3$, plot the y-intercept (0, 3) and use the slope (-1) to find another point, like (1, 2).

4. Determine the shading for the inequalities

For $y < 2x + 1$, shade below the line since it’s a "less than" inequality.

For $y \geq -x + 3$, shade above the line, since it’s a "greater than or equal to" inequality.

5. Find the overlapping region

Look for the area where the shaded regions from both inequalities overlap. This region is the solution set.

6. Select a point in the overlapping region

Finally, choose any point that is within the overlapping region as a solution. For example, the point (0, 2) can be checked to see if it satisfies both inequalities.