Graph the system of inequalities.
Step 1 Solve the first inequality for y. Then graph the inequality.
The first inequality does not contain the variable y.
To graph the first inequality, x ≤ 0, first graph the corresponding
equation, x = 0.
This is a vertical line that passes through the x-axis at the point (0, 0);
it is the y-axis.
For the inequality x ≤ 0, the inequality symbol is ≤.
This stands for is less than or equal to.
To represent equal to, draw a solid line along the y-axis.
To represent less than, shade the region to the left of the line.
Each point in that region has an x-coordinate less than 0.
Step 2 Solve the second inequality for y. Then graph the inequality.
To solve x - 2y > 2 for y, do the following:
, first graph the equation
|Subtract x from both sides.
||- 2y > - x + 2
|Divide both sides by -2. Be sure to
reverse the inequality symbol because
you are dividing by a negative number.
The y-intercept is (0, -1). Plot (0, -1).
The slope is
. To find a second point on the line, start at (0,
move up 1 and right 2 to the point (2, 0). Plot (2, 0).
Since the inequality symbol < does not contain equal to,
draw a dotted line through (0, -1) and (2, 0).
To represent less than, shade the region below the line.
Step 3 Shade the region where the two graphs overlap.
The solution is the region where the graphs overlap.
The solution of the system is the dark
As a check, choose a point in the solution region.
For example, choose ( -1, -5).
To confirm that ( -1, -5) is a solution of the system, substitute -1 for x
and -5 for y in each of the original inequalities and simplify.
≤ 0 ? Yes
x - 2y
-1 - 2(-5)
-1 + 10
> 2 ?
> 2 ?
> 2 ? Yes
Since ( 1, 5) satisfies each inequality, it is a solution of the system.