Q. 301 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing.  

$\left\{\begin{array}{l}y\le -\frac{2}{3}x+5\\ x\ge 3\end{array}\right.$

Step-by-Step Solution

Answer

The darkest region is the solution to the system of equations.

Step 1: Given information

Given system of equations

$\left\{\begin{array}{l}y\le -\frac{2}{3}x+5\\ x\ge 3\end{array}\right.$

Step 2: Graph the system of equations

The system of equations $y=-\frac{2}{3}x+5$ has intercept $x=7.5,y=5$ The boundary is solid.

Step 3: Calculating for second equation

For $x\ge 3$, the intercepts are $x=3,y=0$ and testing the point $(0,0)$, we get

$0\ge 3$ which is false hence, origin is not contained in it.

Step 4: Plotting the graph