Warm Up

1
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2
Warm Up Solve for the indicated variable. 1. P
R C for R 2. V Ah for A 3. R
for C
R P C
Rt S C
3
Problem of the Day At an audio store, stereos
have 2 speakers and home-theater systems have 5
speakers. There are 30 sound systems with a total
of 99 speakers. How many systems are stereo
systems and how many are home-theater systems?
17 stereo systems, 13 home-theater systems
4
Sunshine State Standards
MA.8.A.1.3 Use tables, graphs, and models to
represent, analyze, and solve real-world problems
related to systems of linear equations.
5
(No Transcript)
6
Additional Example 1A Solving Systems of
Equations
Solve the system of equations.
y 4x 6
y x 3
The expressions x 3 and 4x 6 both equal y. So
by the Transitive Property they are equal to each
other.
y 4x 6
y x 3
4x 6 x 3
7
Additional Example 1A Continued
Solve the equation to find x.
4x 6 x 3
x x
Subtract x from both sides.
3x 6 3
6 6
Add 6 to both sides.
3x 9
Divide both sides by 3.
3 3
x 3
To find y, substitute 3 for x in one of the
original equations.
y x 3 3 3 6
The solution is (3, 6).
8
Additional Example 1B Solving Systems of
Equations
y 2x 9
y 8 2x
2x 9 8 2x
Transitive Property Subtract 2x from both sides.
2x 2x
9 ? 8
The system of equations has no solution.
9
Check It Out Example 1A
Solve each system of equations.
y x 5
y 2x 8
x 5 2x 8
y x 5
3 x
y (3) 5 2
The solution is (3, 2).
10
Check It Out Example 1B
Solve each system of equations.
y 2x
y x 6
2x x 6
y 2x
x 6
y 2(6) 12
The solution is (6, 12).
11
When equations in a system are not already solve
for one variable, you can solve both equations
for x or both for y.
12
Additional Example 2A Solving Systems of
Equations by Solving for a Variable
Solve the system of equations.
x 4y 10 x 3y 11
Solve both equations for x.
x 4y 10 x 3y 11
4y 4y 3y
3y
x 10 4y x 11 3y
10 4y 11 3y
10 4y 11 3y
Subtract 3y from both sides.
3y 3y
10 7y 11
13
Additional Example 2A Continued
10 7y 11
Add 10 to both sides.
10 10
7y 21
Divide both sides by 7.
7 7
y 3
x 11 3y
11 3(3) Substitute 3 for y.
11 9 2
The solution is (2, 3).
14
(No Transcript)
15
Additional Example 2B Solving Systems of
Equations by Solving for a Variable
Solve the system of equations.
2x 10y 8 x 5y 4
Solve both equations for x.
2x 10y 8 x 5y 4
10y 10y
5y 5y
2x 8 10y x 4 5y
x 4 5y
Subtract 5y from both sides.
4 5y 4 5y
5y 5y
4 4
Since 4 4 is always true, the system of
equations has an infinite number of solutions.
16
Check It Out Example 2A
Solve each system of equations.
2x y 0 2x 3y 8
-2x 83
y -2x and y
-2x 83
2x x 2
2x y 0
2(-2) y 0
y 4
The solution is (2, 4).
17
Check It Out Example 2B
Solve the system of equations.
y x 1 3x 3y 4
3x 43
y x - 1 and y
3x 43
x 1
-3 ? 4
There are no solutions.
18
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
19
Lesson Quiz
Solve each system of equations. 1. y 5x 10
y 7 5x 2. y 2x 1 y 4x 3. 6x
y 15 2x 3y 5 4. Two numbers have a sum
of 23 and a difference of 7. Find the two
numbers.
no solution
(2, 3)
15 and 8
20
Lesson Quiz for Student Response Systems
1. Solve the given system of equations. y 11x
20 y 2 11x A. (2, 2) B. (1, 1) C. (1,
1) D. no solution
21
Lesson Quiz for Student Response Systems
2. Solve the given system of equations. 4x y
11 2x 3y 7 A. (4, 5) B. (4, 5) C. (2,
5) D. (2, 5)
22
Lesson Quiz for Student Response Systems
3. Two numbers have a sum of 37 and a difference
of 17. Identify the two numbers. A. 27 and
10 B. 27 and 10 C. 27 and 10 D. 27 and 10