Q. 298 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}x-2y<3\\ y\le 1\end{array}\right.$

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 $\left\{\begin{array}{l}x-2y<3\\ y\le 1\end{array}\right.$

Step 2: Checking the point

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

$$\begin{gathered} 0-2\left(0\right)<3 \\ 0-0<3 \\ 0<3 \end{gathered}$$ which is true

So origin is included

Step 3: Checking for another equation

The equation $y\le 1$ .Testing the point $(0,0)$, we get

$0\le 1$ which is true

So origin is included

Step 4: Graph of the system of equation

The graph is