Q 289 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing.

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

Step-by-Step Solution

Answer

The darkest region represent the solution to the system of equations and the graph is 

Step 1: Given information

Given system of equations $\left\{\begin{array}{l}y\ge -\frac{2}{3}x+2\\ y>2x-3\end{array}\right.$

Step 2: Checking the point for system of equation

The equation $y=-\frac{2}{3}x+2$ has intercept $2,3$ . Testing the point $(0,0)$, we get

$$\begin{gathered} 0\ge 0+2 \\ 0\ge 2 \end{gathered}$$ which is not true

So origin is not included

Step 3: Checking the point for system of equations

The equation $y=2x-3$ has intercept $-3,\frac{3}{2}$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0>0-3 \\ 0>-3 \end{gathered}$$ which is not true

So origin is not included

Step 4: Graphing the system of equations

The graph of the system of equations is