Q 294 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}2x-5y<10\\ 3x+4y\ge 12\end{array}\right.$

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 $\left\{\begin{array}{l}2x-5y<10\\ 3x+4y\ge 12\end{array}\right.$

Step 2: Checking the point

The equation, $2 x-5 y=10$ has the intercept $-2,5$ Testing the point $(0,0)$, we get

$$\begin{gathered} 2\left(0\right)-5\left(0\right)<10 \\ 0-0<10 \\ 0<10 \end{gathered}$$ which is true

So origin is included

Step 3: Checking for another equation

The equation, $3 x+4 y=12$ has the intercept $3,4$. Testing the point $(0,0)$, we get

$$\begin{gathered} 3\left(0\right)+4\left(0\right)\ge 12 \\ 0+0\ge 12 \\ 0\ge 12 \end{gathered}$$ which is not true

So origin is not included

Step 4: Graph the equation

The graph is