Graphing Systems of Linear Inequalities: example 5.56

Solve the system by graphing. ${\begin{matrix} y > \frac{1}{2} x - 4 \\ x - 2 y < −4 \end{matrix}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the system by graphing. ${\begin{matrix} y \geq 3 x + 1 \\ −3 x + y \geq −4 \end{matrix}$

How did it go?

Graph $y > \frac{1}{2} x - 4$ by graphing $y = \frac{1}{2} x - 4$ using the slope $m = \frac{1}{2}$ and the intercept b = −4. The boundary line will be dashed. Test (0, 0). It makes the inequality true. So, shade the side that contains (0, 0) red.
Graph $x - 2 y < - 4$ by graphing $x - 2 y = - 4$ and testing a point. The intercepts are x = −4 and y = 2 and the boundary line will be dashed. Choose a test point in the solution and verify that it is a solution to both inequalities.