solve the following system of inequalities graphically on the set of axes below. state the coordinates of a…

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

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

Answer

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.)