Question

I need help graphing systems of inequalities and showing all the possible solutions

Answer 1

Given the system of inequalities

`y>-2x+5`
`y\leq x-3`

To graph an inequality you have to apply a method similar to the one you apply when graphing linear equations.

For each inequality, you have to find at least two points of the line and draw it, then shadow the area corresponding to the inequality.

For the first expression

`y>-2x+5`

First, determine two points to draw the line that determines the minimum value of the inequation.

For x=0

`\begin{gathered} y>-2\cdot0+5 \\ y>5 \end{gathered}`

For x=2

`\begin{gathered} y>-2\cdot2+5 \\ y>1 \end{gathered}`

Once you plotted the line, since the inequality is determined to the values greater than it, you have to shade the area above it.

For the second expression

`y\leq x-3`

For x=0

`\begin{gathered} y\leq0-3 \\ y\leq-3 \end{gathered}`

For x=3

`\begin{gathered} y\leq3-3 \\ y\leq0 \end{gathered}`

With the two points, you can plot the line. Note that the inequality indicates its range is all values equal or less than the line, so you have to shade the area below the line.