Q 291 - Intermediate Algebra

Question

The darkest region represent the solution to the system of equations  $\left\{\begin{array}{l}x+2y<4\\ y<x-2\end{array}\right.$

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

Step 2: Checking the point for the system of equations

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

$$\begin{gathered} 0+0<4 \\ 0<4 \end{gathered}$$ which is true

So origin is included

Step 3: Checking for another equation

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

$$\begin{gathered} 0<0-2 \\ 0<-2 \end{gathered}$$ which is not true

So origin is not included

Step 4: Graph of system of equation

The graph is