Q. 297 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing  $\left\{\begin{array}{l}2x+y>-6\\ -x+2y\ge -4\end{array}\right.$

Step-by-Step Solution

Answer

The darkest region represent the solution to the system of equations    

Step 1: Given information

Given the system of equations $\left\{\begin{array}{l}2x+y>-6\\ -x+2y\ge -4\end{array}\right.$

Step 2: Checking the point

The equation $2x+y=6$ has intercept $6,3$. Testing the point $(0,0)$, we get

$$\begin{gathered} 2\left(0\right)+0>-6 \\ 0+0>-6 \\ 0>-6 \end{gathered}$$ which is true

So origin is included

Step 3: Checking for another equation

The equation $-x+2y=-4$ has intercept $-2,4$ .Testing the point $(0,0)$, we get

$$\begin{gathered} -0+2\left(0\right)\ge -4 \\ 0+0\ge -4 \\ 0\ge -4 \end{gathered}$$ which is true

So origin is included

Step 4: Sketching the graph

The graph is