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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