Lesson Plan 0 - Quia
Algebra 1 Lesson Notes 7.2A _____________________
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
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: A2a: Lesson 7.2 Practice A #1-18
A2b: Lesson 7.2 Practice B #1-15
A2c: pp 439 #3-19 odd
Algebra 1 Lesson Notes 7.2B _____________________
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
c. Solve using substitution:
2x – 3y = 6
9y – 27 = 6x
Identifying the number of solutions without solving:
Step 1: Rewrite the equations in slope-intercept form.
Step 2: Determine the number of solutions:
Different slopes 1 solution
Same slope and No solution
different y-intercepts (lines are parallel)
Same slope and Infinite solutions
same y-intercepts (same line)
Example: Identify the number of solutions without solving
a. [pic]
[pic]
b. y = 3x – 5
2y = 6x – 10
c. 3y + 6x = 8
2x + y = –10
( HW: A3a pp 463 #16, 19, 20, 21, 22*, 26-28 *solve using substitution
Algebra 1 Lesson Notes 7.2C _____________________
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.
Solution 1: ____ Solution 2: ____ Total: ____
Volume x y
Amount
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.
Value 1: ____ Value 2: ____ Total:
Number x y
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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Number of solutions
Slopes and y-intercepts
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