Example

Example 1

Graph the solution to the following system:

\(\begin{align*} x-y< -6\\ 2y\ge 3x+17\end{align*}\)

Solution:

First we will rewrite the equations in slope-intercept form in order to graph them:

Inequality 1 \(\begin{align*} x-y &< -6 \quad \text{Solve for y.}\\ -y& < -x -6 \quad \text{Subtract x from each side.}\\ y & > x+6 \quad \text{Multiply each side by -1, flipping the inequality.}\end{align*}\)

Inequality 2 \( \begin{align*} 2y & \geq 3x+17 < \quad \text{Solve for y.} \\ y & \geq \frac{3}{2}x+8.5 < \quad \text{Divide each side by 2.}\end{align*} \)

Graph each equation and shade accordingly:


Back to '6.8: Applications of Systems of Linear Inequalities'