Question

Solve the following system of inequalities graphically on the set of axes. State the coordinates of a point in the solution set.y < 2x - 5y ≤ - x - 2

Answer 1

Given: The systems of inequalities below

$\begin{gathered} y<2x-5 \\ y\le-x-2 \end{gathered}$

To Determine: The graphical solution of the system of inequalities

Calculate the coordinates of the x-intercept and the y-intercept of the first equation

$\begin{gathered} y<2x-5 \\ x_{i\text{ntercept}},\text{make y = 0} \\ 0=2x-5 \\ 2x=5 \\ x=\frac{5}{2} \\ x_{i\text{ntercept coordinate}}=(\frac{5}{2},0) \\ y_{\text{ intercept, make x=0}} \\ y=2(0)-5 \\ y=0-5=-5 \\ y_{\text{ intercept coordinate}}=(0,-5) \end{gathered}$

Calculate the coordinates of the x-intercept and the y-intercept of the second equation

$\begin{gathered} y\le-x-2 \\ x_{\text{ intercept,make y = 0}} \\ 0=-x-2 \\ x=-2 \\ x_{\text{ intercept coordinate}}=(-2,0) \\ y_{\text{ intercept, make x = 0}} \\ y=-0-2 \\ y=-2 \\ y_{\text{ intercept coordinate}}=(0,-2) \end{gathered}$

Let us graph the solution of the system of inequalities as shown below

Hence, the solution of the system of inequalities is the area shaded purple in the above graph excluding the points at the edges of the broken line for y < 2x -5

For example (5, -5)