Graphing Systems of Linear Inequalities: example 5.55

Solve the system by graphing. ${\begin{matrix} 4 x + 3 y \geq 12 \\ y < - \frac{4}{3} x + 1 \end{matrix}$

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. ${\begin{matrix} 3 x - 2 y \leq 12 \\ y \geq \frac{3}{2} x + 1 \end{matrix}$

How did it go?

Graph $4 x + 3 y \geq 12$ , by graphing $4 x + 3 y = 12$ and testing a point. The intercepts are x = 3 and y = 4 and the boundary line will be solid. Test (0, 0). It makes the inequality false. So, shade the side that does not contain (0, 0) red.
Graph $y < - \frac{4}{3} x + 1$ by graphing $y = - \frac{4}{3} x + 1$ using the slope $m = \frac{4}{3}$ and the y-intercept b = 1. The boundary line will be dashed. Test (0, 0). It makes the inequality true. So, shade the side that contains (0, 0) blue.