Question

Which graph shows the solution to this system of inequalities?
y>-1/3x+1
y>2x-3

Answer 1

Given:

The system of inequalities is:

`y>-(1)/(3)x+1`

`y>2x-3`

To find:

The graph of the given system of inequalities.

Solution:

We have,

`y>-(1)/(3)x+1`

`y>2x-3`

The related equations are:

`y=-(1)/(3)x+1`

`y=2x-3`

Table of values for the given equations is:

`x`
`y=-(1)/(3)x+1`
`y=2x-3`

0 1 -3

3 0 3

Plot (0,1) and (3,0) and connect them by a straight line to get the graph of
`y=-(1)/(3)x+1`.

Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of
`y=2x-3`.

The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.

Therefore, the graph of the given system of inequalities is shown below.