Graphing Systems of Inequalities
5B
When we solved and graphed inequalities with only one variable (ex: x > 3), we moved on
to compound inequalities (AND/OR). We would graph both inequalities on the same number line
and decide what to keep based on whether it was an AND or an OR problem. When we graphed
linear equations on the coordinate plane we moved on to solving systems of equations
graphically.
When we graph inequalities in two variables on the coordinate plane, we do not graph compound
inequalities. We move on to solving systems of inequalities. It takes a little from both
inequalities with one variable and solving systems graphically.
Solve the system of inequalities graphically:
y>¼x+3
y < 3x – 5
Step 1:
Graph and shade the 1st inequality
y>¼x+3
m=
1
(up1)
=
4 (right 4)
m=
3
(up3)
=
1 (right1)
1st pt.= (0,-5)
1st pt= (0,3)
(0, 2)
y>¼x+3
2 > ¼ (0)+3
2 > 3
Step 2: ON THE SAME GRAPH
Graph and shade the 2nd inequality
y < 3x – 5
(0, 4)
y>¼x+3
-3 > ¼ (0) + 3
4>3
FALSE
TRUE
(0-6)
y < 3x – 5
-6 < 3(0) - 5
-6 < -5
(0,-4)
y < 3x – 5
-4 < 3(0) - 5
-4 < -5
TRUE
FALSE
Step 3: Label the area where the shading intersects with an “S”
1) y < ⅓x – 4
y > -5x + 1
2) 4x + 2y ≤ 4
5x – 3y < 9
3) 2x + 12y > 36
4) x ≥ 4
11x – 33y ≥ 66
(y – 3) >
5) 42x – 14y < 56
6) (y – 2) >
y ≥ -2
1
(x – 2)
2
3
(x – 4)
4
15x + 9y ≤ 27
Name ______________________________________
Date _____________
Algebra I – Pd ____
Graphing Systems of Linear Inequalities
Graph the following systems, show all work on looseleaf
1) y≥ 3x + 1
y–1<x
2) 2y≥ x – 4
y < 3x
3) -2y ≥ -4x – 6
y≥x
4) x + y > 6
y ≤ 2x – 5
5) y – 4 > -2x
y>x+2
6) 2x – y ≤ 3
3x + y ≤ 7
7) y > -2x + 10
3x + y < 7
8) y ≤ x -3
-y – x < -1