Presentation on theme: "Warm Up Evaluate each expression for x = 1 and y =–3."— Presentation transcript:
1 Warm UpEvaluate each expression for x = 1 and y =–3.1. x – 4y –2x + yWrite each expression in slope-intercept form.3. y – x = 14. 2x + 3y = 65. 0 = 5y + 5x13–5y = x + 1y = x + 2y = –x
2 ObjectivesIdentify solutions of linear equations in two variables.Solve systems of linear equations in two variables by graphing.
3 Vocabulary systems of linear equations solution of a system of linear equations
4 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.
5 Example 1A: Identifying Solutions of Systems Tell whether the ordered pair is a solution of the given system.(5, 2);3x – y = 132 – 2 00 03(5) –15 –3x – y =13Substitute 5 for x and 2 for y in each equation in the system.The ordered pair (5, 2) makes both equations true.(5, 2) is the solution of the system.
6 Example 1B: Identifying Solutions of Systems Tell whether the ordered pair is a solution of the given system.x + 3y = 4(–2, 2);–x + y = 2–2 + 3(2) 4x + 3y = 4–4 4–x + y = 2–(–2)4 2Substitute –2 for x and 2 for y in each equation in the system.The ordered pair (–2, 2) makes one equation true but not the other.(–2, 2) is not a solution of the system.
7 All solutions of a linear equation are on its graph 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 – 1y = –x + 5The 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.
8 Example 2A: Solving a System by Graphing Solve the system by graphing. Check your answer.y = xGraph the system.y = –2x – 3The solution appears to be at (–1, –1).CheckSubstitute (–1, –1) into the system.y = xy = –2x – 3(–1) –2(–1) –3– – 3–1 – 1y = x(–1) (–1)–1 –1•(–1, –1)y = –2x – 3The solution is (–1, –1).
9 Check It Out! Example 2a Solve the system by graphing. Check your answer.y = –2x – 1Graph the system.y = x + 5The solution appears to be (–2, 3).Check Substitute (–2, 3) into the system.y = x + 5y = –2x – 1y = –2x – 13 –2(–2) – 1– 1y = x + 53 –2 + 53 3The solution is (–2, 3).
10 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?
11 Example 3 Continued1Make a PlanWrite 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.Totalpagesisnumber readeverynightplusalready read.Wreny=2 x+14Jenniy=3 x+6
12 Example 3 Continued 2 Solve 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.(8, 30)Nights
13 Example 3 Continued Look Back 3 Check (8, 30) using both equations.Number of days for Wren to read 30 pages.2(8) + 14 = = 30Number of days for Jenni to read 30 pages.3(8) + 6 = = 30
14 Check It Out! Example 3Video club A charges $10 for membership and $3 per movie rental. Video club B charges $15 for membership and $2 per movie rental. For how many movie rentals will the cost be the same at both video clubs? What is that cost?
15 Check It Out! Example 3 Continued 1Make a PlanWrite a system of equations, one equation to represent the cost of Club A and one for Club B. Let x be the number of movies rented and y the total cost.Totalcostispricefor eachrentalplusmember-ship fee.Club Ay=3 x+10Club By=2 x+15
16 Check It Out! Example 3 Continued Solve2Graph y = 3x + 10 and y = 2x The lines appear to intersect at (5, 25). So, the cost will be the same for 5 rentals and the total cost will be $25.
17 Check It Out! Example 3 Continued Look Back3Check (5, 25) using both equations.Number of movie rentals for Club A to reach $25:3(5) + 10 = = 25Number of movie rentals for Club B to reach $25:2(5) + 15 = = 25
18 Lesson Quiz: Part ITell whether the ordered pair is a solution of the given system.1. (–3, 1);2. (2, –4);noyes
19 Lesson Quiz: Part IISolve 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. After how many months will they have the same number of stamps? How many will that be?y + 2x = 9(2, 5)y = 4x – 34 months13 stamps
20 Make a Graphic Organizer Must foldMust have colorMust write out the problem and include somewhere in the organizerMust show all 3 methods of solving the problem in the organizer(Hint: All 3 answers should be the same!)Be Creative!