Question

For each system: put into y intercept. Find the y intercept and sketch the graph.

Answer 1

`\begin{gathered} 4x-3y<-3 \\ \text{The y-intercept is derived when x=0. Therefore} \\ \text{Make y the subject of the inequality} \\ -3y<-3-4x \\ -3y<-3-4(0) \\ -3y<-3 \\ \text{Divide both sides by -3} \\ y>1 \\ \text{The graph is shown below;} \end{gathered}`

Number (2)

`\begin{gathered} -x+3y>-6 \\ \text{Make y the subject of the inequality} \\ 3y>-6+x \\ 3y>-6+0 \\ 3y>-6 \\ \text{Divide both sides by 3} \\ y>-2 \\ \text{The graph is also shown below;} \end{gathered}`

Observe that for the first inequality, the y intercept is 1, that is, the graph crosses the y axis at the point where y = 1. Hence all values of the inequality lies at the point where y > 1 (as shown by the shaded region)

Similarly, for the second inequality, the y intercept is -2. Hence all the values of the inequality lies at the shaded region where all values of y is greater than -2