The document provides examples of solving systems of linear equations by substitution and elimination. It also demonstrates how to graph systems of linear inequalities by writing each inequality in slope-intercept form, determining whether the line is solid or dashed, and shading the appropriate regions. Finally, it shows how to apply systems of equations to word problems by setting up the corresponding equations and solving.

2. Warm Up: (3)
2. What is the solution to the following system of equations:
2(m + n) + m = 9
3m - 3n = 24

3. Warm Up: A Note about Solving by Elimination
4) Substitute into ANY
original equation.
2x + 3y = 12
-2 = 5y – 4x
2
2
2) Make
opposites.
2
2 x 3 y 12
4x 5 y
2 x 3 y 12
2
2x 3 2 12
2x 6 12
6 6
2x 6
4x 6y 24
4x 5 y
2
11y 22
11
y
2
11
2
1) Arrange
the variables.
3, 2
2
x 3
3) Add and
solve for the
variable.
5) Check your
answer.

4. Class Notes: Systems of Inequalities(3)
• Steps to Graphing Linear System Inequalities
1. Write the equation in slope-intercept form.
2. Graph the y-intercept and slope.
3. Draw the line (solid or dashed).
,
Dashed line
,
Solid line
4. Lightly shade above or below the y-intercept.
,
Above y-intercept
,
Below y-intercept
5. Graph the other equation. See #’s 3 and 4
6. Darkly shade overlap.

5. Class Notes: Systems of Inequalities
Graph the system of linear inequalities.
Ex.
2
2
b
1 Solid
y
x 1 m
3
3
y
m
4
x 5
3
4
b 5
3
Dashed
Above
Below
1) Put in
slope-intercept
form.
2) Graph.
Find m and b.
3) Solid or
dashed?
4) Lightly
shade above
or below the
y-intercept?
5) Do the same
for the other
equation.
6) Darkly
shade overlap.

6. Graph the system of linear inequalities.
1) Put in slopeintercept form.
y
y
m
1
m
x 5
2
3x 2
3
b
1
Dashed
Above
2
1
2
b
5 Dashed
Above
2) Find m and
b, then graph
3) Solid or
dashed?
4) Lightly
shade above
or below the
y-intercept?
5) Do the same
for the other
equation.
6) Darkly
shade overlap.

7. Write the system of inequalities that produced this graph.

8. Applying Systems of Equations (1)
Ex. Timmy has a pocket full of quarters and dimes. There are a
total of 40 coins. When he added it up he counted $5.50. How
many quarters does he have in his pocket?
10
x = # of
quarters
10
x y 40
.25x .10 y 5.50
100
y = # of
dimes
10
100
15x 150
Substitute into ANY
original equation.
15
1. Mark
the text.
2. Label
variables.
100
25x 10 y 550
10x 10 y
400
15
Let’s eliminate
the ‘Y’
x y 40
10 y 40
10
10
y 30
x 10
10 quarters
3. Create
equations.
4. Solve.

9. Notes
Graph the system of linear inequalities.
Ex.
2x y
4
x 2 y 12
2x y
2x
y
m
x 2 y 12
x
x
4
2x
2x 4
2
b
1
Dashed
Above
2y
2
4
y
m
x 12
2 2
1
x 6
2
1
b 6
2
Solid
Below

10. Notes
Graph the system of linear inequalities.
Ex.
3x 2 y 8
6 x 2 y 10
3x 2 y 8
3x
3x
6 x 2 y 10
6x
6x
2y
2
2y
6 x 10
2
2 2
y 3x 5
y
m
3x 8
2
2
3
x 4
2
3
b
2
4
m
3
b
1
Solid
Dashed
Below
Above
5

11. Class Work/Test Review:
See Handout

12. Check It Out! Example 3 Continued
2
Make a Plan
Write a system of equations, one equation to
represent the cost of Club A and one for Club B.
Let x be the number of movies rented and y the
total cost.
Total
cost
is price
for each
rental
plus
membership fee.
Club A
y
=
3
x
+
10
Club B
y
=
2
x
+
15