Question

question 12, 7.4.25 graph the solution set of the given system of linear inequalities. 5x + y < 10 x - y > 3 use the graphing tool to graph the system. click to enlarge graph

Explanation:

Step1: Rewrite inequalities in slope - intercept form

For $5x + y<10$, we get $y < - 5x + 10$. The boundary line is $y=-5x + 10$, which has a y - intercept of 10 and a slope of - 5. Since the inequality is $y < - 5x + 10$, we will draw a dashed line (because the inequality is strict) and shade the region below the line.
For $x - y>3$, rewrite it as $y

Step2: Find the intersection of the shaded regions

The solution set of the system of inequalities is the region that is shaded for both inequalities. This is the region that is below the line $y=-5x + 10$ and below the line $y=x - 3$.

Answer:

The solution set is the intersection of the region below the line $y=-5x + 10$ and the region below the line $y=x - 3$, represented by the doubly - shaded region (with dashed boundary lines for both inequalities).