Systems of equations and Matrice

Question

Graph the following system of inequalities:

Answer 1

First turn them into "y = ":

3x - y < -1

-y < -3x - 1

y > 3x + 1

y + 3 ≥ x²

y ≥ x² - 3

Then graph the "equalities" - these will be the boundaries. The line y = 3x + 1 will be a dashed line because it is ">? than the line (the points on the boundary are not included. The parabola y = x² - 3 will be a solid line because, since it is "≥" the boundary is included in the solution.

Then shade appropriately. For the line y - 3x + 1 you shade above the boundary line because y is greater than the boundary. For the parabola y = x² - 3 you also shade above the boundary.

The solution is the purplish portion.