Question

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

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

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

Checking the point

The equation, $2x-5y=10$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

Checking for another equation

The equation, $3x+4y=12$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

Graph the equation

The graph is