Answer:
(4,-2)
(1, 1)
(0, 0)
Explanation:
To change it to the y-intercept form, we need to solve each inequality for y, so:
2x + 3y > -3
2x + 3y - 2x > -3 - 2x
3y > -3 - 2x
3y/3 > -3/3 - 2x/3
y > - 1 - 2x/3
2x - 3y > -9
2x - 3y - 2x > -9 - 2x
-3y > -9 - 2x
-3y/(-3) < -9/(-3) - 2x/(-3)
y < 3 + 2x/3
We change the sign of the inequality because we divide by a negative number.
Then, to sketch the graph, we need to identify the lines that divide the regions and two points of these lines, so:
For y > - 1 - 2x/3:
We get that the line that divides the region is: y = - 1 - 2x/3
And two points that belong to this line are (0, -1) and (3, -3)
For y < 3 + 2x/3:
The line is: y = 3 + 2x/3
and the points are (0, 3) and (-3, 1)
So, the graph of the system of inequalities is:
Therefore, the yellow region is the solution of the system and the correct solution are the points that belong to that region.
Then, the answers are:
(4, -2), (1, 1) and (0, 0)
