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:

$y>-\dfrac{1}{3}x+1$

$y>2x-3$

To find:

The graph of the given system of inequalities.

Solution:

We have,

$y>-\dfrac{1}{3}x+1$

$y>2x-3$

The related equations are:

$y=-\dfrac{1}{3}x+1$

$y=2x-3$

Table of values for the given equations is:

    $x$                   $y=-\dfrac{1}{3}x+1$             $y=2x-3$

   0                             1                              -3

   3                             0                              3

Plot (0,1) and (3,0) and connect them by a straight line to get the graph of $y=-\dfrac{1}{3}x+1$.

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.