Q. 302 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

$\left\{\begin{array}{l}y\ge \frac{3}{4}x-2\\ y<2\end{array}\right.$

Step-by-Step Solution

Answer

In the following exercises, solve each system by graphing.  

Step 1: Given information

Given system of equation

$\left\{\begin{array}{l}y\ge \frac{3}{4}x-2\\ y<2\end{array}\right.$

Step 2: Graph the system of equations

The system of equations $y=\frac{3}{4}x-2$ has intercept $x=2.6,y=-2$ The boundary is solid. Origin lies within as putting $$\begin{gathered} (0,0) \\ 0\ge -2 \end{gathered}$$

which holds true.

Step 3: Calculating for second equation

For $y<2$, the intercepts are $x=0,y=2$ and testing the point $(0,0)$, we get

$0<2$ which is true hence, origin is contained in it.

Step 4: Plotting the graph