1.
Warm Up: (3)
2. What is the solution to the following system of equations:
2(m + n) + m = 9
3m - 3n = 24
2.
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.
3.
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.
4.
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.
5.
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.
6.
Write the system of inequalities that produced this graph.
7.
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.
8.
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
9.
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.
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
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