Question

solve the following system of inequalities graphically on the set of axes below. state the coordinates of a point in the solution set. $y \leq -\frac{3}{5}x + 7$ $y < 2x - 6$

Explanation:

Step1: Understand the inequalities

We have two inequalities: \( y \leq -\frac{3}{5}x + 7 \) and \( y < 2x - 6 \). We need to find a point that satisfies both. Let's pick a point in the shaded region. Looking at the graph, let's check \( (5, 0) \).

Step2: Check first inequality

Substitute \( x = 5 \), \( y = 0 \) into \( y \leq -\frac{3}{5}x + 7 \):
\( 0 \leq -\frac{3}{5}(5) + 7 \)
\( 0 \leq -3 + 7 \)
\( 0 \leq 4 \), which is true.

Step3: Check second inequality

Substitute \( x = 5 \), \( y = 0 \) into \( y < 2x - 6 \):
\( 0 < 2(5) - 6 \)
\( 0 < 10 - 6 \)
\( 0 < 4 \), which is true.

Answer:

\((5, 0)\) (Other valid points in the shaded region are also acceptable, e.g., \((4, -1)\), \((6, 1)\) etc.)