Solving Systems by Graphing 5-1 Solving Systems by Graphing Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1
Warm Up 11/01/16 Evaluate each expression for x = 1 and y =–3. 1. x – 4y Write each expression in slope-intercept form. 2. y – x = 1
Essential Objectives 1. Identify solutions of linear equations in two variables. 2. Solve systems of linear equations in two variables by graphing.
Vocabulary A system of linear equations is a set of two or more linear equations (two or more variables). A solution of a system of linear equations 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.
3x – y = 13
Example: Identifying Solutions of Systems Is the ordered pair is a solution or not? (5, 2); 3x – y = 13 2 – 2 0 0 0 3(5) – 2 13 15 – 2 13 13 13 3x – y =13 (5, 2) is the solution of the system.
If an ordered pair does not satisfy the first equation in the system, there is no reason to check the other equations. Helpful Hint
Example Is the ordered pair is a solution or not? x + 3y = 4 (–2, 2); –x + y = 2 –2 + 3(2) 4 x + 3y = 4 –2 + 6 4 4 4 –x + y = 2 –(–2) + 2 2 4 2 (–2, 2) is not a solution of the system.
I do…… Is the ordered pair is a solution or not? (1, 3); 2x + y = 5 –2x + y = 1 2x + y = 5 2(1) + 3 5 2 + 3 5 5 5 –2x + y = 1 –2(1) + 3 1 –2 + 3 1 1 1 (1, 3) is the solution of the system.
You do…. Is the ordered pair is a solution or not? x – 2y = 4 (2, –1); 3x + y = 6 x – 2y = 4 2 – 2(–1) 4 2 + 2 4 4 4 3x + y = 6 3(2) + (–1) 6 6 – 1 6 5 6 (2, –1) is not a solution of the system.
Remember: 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.
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
Example: Solving a System by Graphing Solve the system by graphing. Check your answer. y = x y = –2x – 3 Graph the system.
y = x Graph the system y = –2x – 3 (–1, –1). Sometimes, it is hard to graph and identify the solution, so………………….
y = x y = –2x – 3 Check Substitute (–1, –1) into the system. y = x (–1) (–1) –1 –1 y = –2x – 3 (–1) –2(–1) –3 –1 2 – 3 –1 – 1 The solution is (–1, –1).
Example Solve the system by graphing. Check your answer. y = –2x – 1 y = x + 5 Graph the system.
Graph the system y = –2x – 1 y = x + 5 (–2, 3). Sometimes, it is hard to graph and identify the solution, so………………….
y = –2x – 1 y = x + 5 y = –2x – 1 Check Substitute y = x + 5 3 –2(–2) – 1 3 4 – 1 3 3 Check Substitute (–2, 3) into the system. y = x + 5 3 –2 + 5 3 3 The solution is (–2, 3).
Solve the system by graphing. Check your answer. Example Solve the system by graphing. Check your answer. Graph using a calculator and then use the intercept command. 2x + y = 4 Rewrite the second equation in slope-intercept form. 2x + y = 4 2x + y = 4 –2x – 2x y = –2x + 4
Example: continuation Check Substitute (3, –2) into the system. 2x + y = 4 –2 (3) – 3 –2 1 – 3 –2 –2 2x + y = 4 2(3) + (–2) 4 6 – 2 4 4 4 The solution is (3, –2).
Example: 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. Write the system that would describe the problem.
Example: Continued Wren y = 2 x + 14 Jenni y = 3 x + 6 y = 2x + 14 y = 3x + 6
Example Video club A charges $10 for membership and $3 per movie rental. Video club B charges $15 for membership and $2 per movie rental. Write the system for the problem.
Club A y = 3 x + 10 Club B y = 2 x + 15 y = 3x + 10 y = 2x + 15
Lesson Quiz: Part I Tell whether the ordered pair is a solution of the given system. 1. (–3, 1); 2. (2, –4);
Lesson Quiz: Part II Solve the system by graphing. 3. 4. Joy has 5 collectable stamps and will buy 2 more each month. Ronald has 25 collectable stamps and will sell 3 each month. Write the system. y + 2x = 9 y = 4x – 3