Q 312 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

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

Step-by-Step Solution

Answer

The solution of the equation is the dark shaded region.

Step 1: Given information.

Given system of equation, 

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

Step 2: Graph the system of equations

The system of equation $y=-3x+2$ 

has intercept $x=0.6,y=2$. The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0\ge 2 \end{gathered}$$

which holds false.

Step 3: Calculating for second equation

For $3x+y=5$,

the intercepts are $x=1.6,y=5$ and testing the point ,

we get

$0>5$,

which is false hence, the origin is not contained in it.

Step 4: Plotting the graph.