Download Algebra 1 Lesson Notes 7.2

Algebra 1
Lesson Notes 7.2A
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Objective: Solve a system of linear equations using substitution.
Solving a system of equations using substitution:
Step 1:
Take inventory of the system of equations.
If necessary, solve one of the equations to get one of its
variables alone.
When possible, isolate the variable that already has a coefficient of 1 or −1.
Step 2:
Substitute the expression from Step 1 into the other equation
and solve for the remaining variable.
Step 3:
Substitute the value from Step 2 into the revised equation
from Step 1 and solve.
Step 4:
Check your solution for accuracy.
Example 1 (p 435): Use the substitution method (without Step 1)
Solve the linear system.
a.
y = 2x – 3
x + 3y = 5
b.
y = –2x + 5
y = 26x – 2
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Example 2 (p 436): Use the substitution method (with Step 1)
Solve the system of equations.
a.
–5y – x = 12
3y – 5x = 4
b.
4x – 2y = 10
3y = 9x – 6
 HW:
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A2a: Lesson 7.2 Practice A #1-18
A2b: Lesson 7.2 Practice B #1-15
A2c: pp 439 #3-19 odd
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Algebra 1
Lesson Notes 7.2B
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Objective: Determine the number of solutions to a system of linear equations using
substitution.
A system of equations may have:
1 solution ↔ solving by substitution results in values for x and y
no solution ↔ solving by substitution results in a false statement
infinite solutions ↔ solving by substitution results in a statement that is
always true
Example: Identify the number of solutions to a system of equations.
a.
Solve using substitution:
2x – 6y = 10
18y = 6x + 30
b.
Solve using substitution:
4x – 2y = 8
y = 2x – 4
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c.
Solve using substitution:
2x – 3y = 6
9y – 27 = 6x
Identifying the number of solutions without solving:
Step 1:
Step 2:
Rewrite the equations in slope-intercept form.
Determine the number of solutions:
Slopes and y-intercepts
Number of solutions
Different slopes
1 solution
Same slope and
different y-intercepts
No solution
(lines are parallel)
Same slope and
same y-intercepts
Infinite solutions
(same line)
Example: Identify the number of solutions without solving
a.
1
y  x3
2
y  2 x  3
b.
y = 3x – 5
2y = 6x – 10
c.
3y + 6x = 8
2x + y = –10
 HW:
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A3a pp 463 #16, 19, 20, 21, 22*, 26-28
*solve using substitution
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Algebra 1
Lesson Notes 7.2C
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Objective: Use substitution to solve multi-step problems involving systems of equations.
Example 3 (p 437): Solve a multi-step problem
A food cooperative is a business that usually offers special prices on locally grown food
and produce. Some cooperative are clubs and others are retail stores. The weekly costs
for seasonal produce offered by a club-based food cooperative and a store-based
cooperative are shown in the table. Find the number of weeks at which the total cost of
weekly produce will be the same.
type of cooperative
club fee ($)
cost per week ($)
club
20
15
retail
none
17.50
Example 4 (p 438): Solve a mixture problem
A.
A chemist needs 15 liters of a 60% alcohol solution. The chemist has solution that is 50%
alcohol. How many liters of the 50% solution and pure alcohol should the chemist mix
together to make 15 liters of a 60% solution?
To solve: Organize the data in a table.
Volume
Solution 1: ____
Solution 2: ____
x
y
Total: ____
Amount
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B.
How many quarts of 100% antifreeze and 50/50 antifreeze/water mix should be combined
to make 16 quarts of a 70/30 antifreeze/water mix?
Example 5: Solve a mixture of coins problem
If you have a total of 41 nickels and quarters and their value is $6.45, how many of each
type of coin do you have?
To solve: You could organize the data in a table.
Number
Value 1: ____
Value 2: ____
x
y
Total:
Amount
 HW:
A3b pp 440-441 #31, 33, 35, 37*
*solve using substitution
Prepare for Quiz 7.1-7.2, 7.5
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