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Holt Algebra 1
6-1 Solving Systems by Graphing6-1 Solving Systems by Graphing
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
6-1 Solving Systems by Graphing
Bell Quiz 6-1Evaluate each expression for x = 1 and y =–3.
1. x – 4y
Write each expression in slope-intercept form.
2. y – x = 1
2 pts
3 pts
5 pts
possible
Holt Algebra 1
6-1 Solving Systems by Graphing
Identify solutions of linear equations in two
variables.
Solve systems of linear equations in two variables by graphing.
Objectives
Holt Algebra 1
6-1 Solving Systems by Graphing
systems of linear equations
solution of a system of linear equations
Vocabulary
Holt Algebra 1
6-1 Solving Systems by Graphing
A system of linear equations is a set of two or more linear equations containing two or more variables. A solution of a system of linear equations with two variables is an ordered pair that satisfies each equation in the system. So, if an ordered pair is a solution, it will make both equations true.
Holt Algebra 1
6-1 Solving Systems by Graphing
Tell whether the ordered pair is a solution of the given system.
Example 1A: Identifying Systems of Solutions
(5, 2);
3x – y = 13
Holt Algebra 1
6-1 Solving Systems by Graphing
If an ordered pair does not satisfy the first equation in the system, there is no reason to check the other equations.
Helpful Hint
Holt Algebra 1
6-1 Solving Systems by Graphing
Example 1B: Identifying Systems of Solutions
Tell whether the ordered pair is a solution of the given system.
(–2, 2);x + 3y = 4
–x + y = 2
Holt Algebra 1
6-1 Solving Systems by Graphing
Check It Out! Example 1a
Tell whether the ordered pair is a solution of the given system.
(1, 3); 2x + y = 5
–2x + y = 1
Holt Algebra 1
6-1 Solving Systems by Graphing
Check It Out! Example 1b
Tell whether the ordered pair is a solution of the given system.
(2, –1); x – 2y = 43x + y = 6
Holt Algebra 1
6-1 Solving Systems by Graphing
All solutions of a linear equation are on its graph. To find a solution of a system of linear equations, you need a point that each line has in common. In other words, you need their point of intersection.
y = 2x – 1
y = –x + 5
The point (2, 3) is where the two lines intersect and is a solution of both equations, so (2, 3) is the solution of the systems.
Holt Algebra 1
6-1 Solving Systems by Graphing
Sometimes it is difficult to tell exactly where the lines cross when you solve by graphing. It is good to confirm your answer by substituting it into both equations.
Helpful Hint
Holt Algebra 1
6-1 Solving Systems by Graphing
Solve the system by graphing. Check your answer.
Example 2A: Solving a System Equations by Graphing
y = x
y = –2x – 3
Holt Algebra 1
6-1 Solving Systems by Graphing
Solve the system by graphing. Check your answer.
Example 2B: Solving a System Equations by Graphing
2x + y = 4
Holt Algebra 1
6-1 Solving Systems by Graphing
Solve the system by graphing. Check your answer.Check It Out! Example 2a
y = –2x – 1
y = x + 5
Holt Algebra 1
6-1 Solving Systems by Graphing
Example 3: Problem-Solving Application
Wren and Jenni are reading the same book. Wren is on page 14 and reads 2 pages every night. Jenni is on page 6 and reads 3 pages every night. After how many nights will they have read the same number of pages? How many pages will that be?
Holt Algebra 1
6-1 Solving Systems by Graphing
1 Understand the Problem
The answer will be the number of nights it takes for the number of pages read to be the same for both girls. List the important information:
Wren on page 14 Reads 2 pages a night
Jenni on page 6 Reads 3 pages a night
Example 3 Continued
Holt Algebra 1
6-1 Solving Systems by Graphing
2 Make a Plan
Write a system of equations, one equation to represent the number of pages read by each girl. Let x be the number of nights and y be the total pages read.
Totalpages is
number read
everynight plus
already read.
Wren y = 2 • x + 14
Jenni y = 3 • x + 6
Example 3 Continued
Holt Algebra 1
6-1 Solving Systems by Graphing
Solve3
Example 3 Continued
•
(8, 30)
Nights
Graph y = 2x + 14 and y = 3x + 6. The lines appear to intersect at (8, 30). So, the number of pages read will be the same at 8 nights with a total of 30 pages.
Holt Algebra 1
6-1 Solving Systems by Graphing
Look Back4
Check (8, 30) using both equations.
Number of days for Wren to read 30 pages.
Number of days for Jenni to read 30 pages.
Example 3 Continued
Holt Algebra 1
6-1 Solving Systems by Graphing
HOMEWORK�Section 6-1 (page 386) 2, 5, 9-13, 28, 29, 33-35 (5, 12, 13: Graph to solve and (5, 12, 13: Graph to solve and (5, 12, 13: Graph to solve and (5, 12, 13: Graph to solve and enter answer in online)enter answer in online)enter answer in online)enter answer in online)
Holt Algebra 1
6-1 Solving Systems by Graphing
HOMEWORK
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