Final answer:
To graph the solution to the system of inequalities 7x+5y ≥ -5 and -7x+3y ≤ 6, we need to graph each inequality separately and find the overlapping region. One point in the solution set can be found by selecting any point within the overlapping region.
Step-by-step explanation:
To graph the solution to the system of inequalities, we need to graph each inequality separately and then find the overlapping region. Let's start with the first inequality, 7x + 5y ≥ -5:
Step 1: Rewrite the inequality in slope-intercept form:
5y ≥ -7x - 5
y ≥ -7/5x - 1
Step 2: Graph the equation y = -7/5x - 1, which is a straight line with a y-intercept of -1 and a slope of -7/5.
Step 3: Shade the region above the line (since y is greater than or equal to -7/5x - 1).
Next, let's graph the second inequality, -7x + 3y ≤ 6:
Step 1: Rewrite the inequality in slope-intercept form:
3y ≤ 7x + 6
y ≤ 7/3x + 2
Step 2: Graph the equation y = 7/3x + 2, which is a straight line with a y-intercept of 2 and a slope of 7/3.
Step 3: Shade the region below the line (since y is less than or equal to 7/3x + 2).
The solution to the system of inequalities is the overlapping region of the two shaded areas. The coordinates of one point in the solution set can be found by selecting any point within the overlapping region.