graph the solution to the following system of inequalities.\n$y\\geq -3x - 5$\n$y < 4x + 7$
graph the solution to the following system of inequalities.\n$y\\geq -3x - 5$\n$y < 4x + 7$
Answer
Explanation:
Step1: Graph (y = - 3x-5)
Since (y\geq - 3x - 5), draw a solid line (because of (\geq)). Find two points: when (x = 0), (y=-5); when (y = 0), (0=-3x - 5), (x=-\frac{5}{3}). Shade above the line.
Step2: Graph (y = 4x + 7)
Since (y<4x + 7), draw a dashed line (because of ( <)). Find two points: when (x = 0), (y = 7); when (y = 0), (0=4x+7), (x=-\frac{7}{4}). Shade below the line.
Step3: Find the intersection region
The solution of the system is the region that is shaded for both inequalities.
Answer:
The solution is the region that is above the solid line (y=-3x - 5) and below the dashed line (y = 4x+7).