“Where the Points Lie”
Systems of Linear
Inequalities
Systems of Inequalities
Standard Form Guided Practice
Graph 2x + 3y < 15 and 2x – 3y > 12 and shade the
solution set.
To review methods of graphing inequalities from
standard form, graph 2x + 3y < 15 by finding the
x-and y-intercepts and 2x – 3y > 12 by solving the
inequality for y.
Systems of Inequalities
Standard Form Review
Graph 2x + 3y < 15 using x- and
y-intercepts.
x-intercept is (x, 0)
y-intercept is (0, y)
2x + 3(0) = 15 2(0) + 3y = 15
3y = 15
2x = 15
y=5
x = 7.5
(0, 5)
(7.5, 0)
Remember, the “greater than”
and “less than” inequalities
have dashed boundary lines.
Systems of Inequalities
Standard Form Review
Test a coordinate on either
side of the line to see where
to shade.
Try (0, 0)
2(0) + 3(0) < 15
Substitute
0 + 0 < 15
Simplify
0 < 15
Simplify
This is true, so shade on the
side of the test point.
Systems of Inequalities
Standard Form Review
(0, –4)
Graph 2x – 3y > 12 by solving
the inequality for y. Test points
to verify shading.
2 x  3 y  12
 3 y  2 x  12
 3 y  2 x  12

3
3
y  32 x  4
What is the y-intercept?
What is the slope?
Is the boundary line dashed or
solid?
Systems of Inequalities
Standard Form Review
Test a coordinate on either side
of the line to see where to
shade.
Try (0, 0)
2(0) – 3(0) > 12
0 + 0 > 12
0 > 12
This is not true, so shade on
the side opposite the test point.
Systems of Inequalities
Standard Form Review
Shade the intersection of the
two solution sets.