Solving Systems of Equations by Graphing Algebra 1

Solving Systems of Equations by Graphing Algebra 1 ~ Chapter 7. 1

Solving Systems by Graphing ** A system of linear equations is a set of two or more linear equations containing two or more variables and connected with a bracket. ** 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.

Solving byare Graphing All solutions of a. Systems linear equation 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 = 2 x – 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.

Solving Systems by Graphing Checking to make sure you graphed the lines correctly, therefore checking for SURE your answer. y = 2 x – 1 y = –x + 5 In the previous slide we graphed the 2 lines and found (2, 3) to be the solution. Check your answer by plugging in (2, 3) to each line. y = 2 x – 1 y = -x + 5 3 = 2(2) – 1 3 = -(2) + 5 3=4– 1 3 = -2 + 5 3=3

by Graphing Ex. 1 -Solving Solve the. Systems system by graphing, then check your solution. y=x y = – 2 x – 3 The solution appears to be at (– 1, – 1). y=x • y = – 2 x – 3 Check Substitute (– 1, – 1) into the system. y=x y = – 2 x – 3 (– 1) – 1 (– 1) – 2(– 1) – 3 – 1 2– 3 – 1 The solution is (– 1, – 1).

by Graphing Ex. 2 Solving - Solve the. Systems system by graphing. Check your solution. y = – 2 x – 1 y=x+5 y = – 2 x – 1 The solution appears to be (– 2, 3). Check Substitute (– 2, 3) into the system. y = – 2 x – 1 y=x+5 3 3 3 – 2 + 5 3 3 3 – 2(– 2) – 1 4 – 1 3 The solution is (– 2, 3).

Systems Graphing Ex. 3 Solving - Solve the system byby graphing. Check your answer. 2 x + y = 4 Rewrite the second equation in slope-intercept form. y = – 2 x + 4 2 x + y = 4 – 2 x y = – 2 x + 4 The solution appears to be (3, – 2).

Solving Systems by Graphing Example 3 Continued …. CHECK 2 x + y = 4 Check Substitute (3, – 2) into the system. Into the ORIGINAL equations. 2 x + y = 4 – 2 – 2 2(3) + (– 2) 4 (3) – 3 6– 2 4 4 4 1– 3 – 2 The solution is (3, – 2).

Solving Systems by Graphing Ex. 4 - Tell whether the ordered pair is a solution of the given system. x + 3 y = 4 4 (– 2, 2); –x + y = 2 x + 3 y = 4 – 2 + (3)2 4 – 2 + 6 4 4 4 –x + y = 2 Substitute – 2 for x and 2 for y. –(– 2) + 2 2 4 2 The ordered pair (– 2, 2) makes one equation true, but not the other. (-2, 2) is NOT a solution of this system.

Systems by Graphing Ex. 5 Solving - Tell whether the ordered pair is a solution of the given system. (5, 2); 3 x – y = 13 0 2– 2 0 0 0 Substitute 5 for x and 2 for y. 3(5) – 2 15 – 2 13 13 The ordered pair (5, 2) makes both equations true, (5, 2) is the solution of this system.

Solving Systems by Graphing Number of Solutions

bythe Graphing Ex. 6 Solving – Number of. Systems solutions. Use graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. ) y = -x + 5 y=x– 3 One solution Consistent/independent b. ) y = -x + 5 No solutions Inconsistent 2 x + 2 y = -8 c. ) 2 x + 2 y = -8 y = -x - 4 Infinitely many solutions Consistent/Dependent

Solving by. Application Graphing Ex. 7: Systems Problem-Solving 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? Wren p = 2 n + 14 Jenni p = 3 n + 6

Solving. Example Systems by Graphing 7 Continued Graph p = 2 n + 14 and p = 3 n + 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

Solving. Example Systems by Graphing 7 Continued Check (8, 30) using both equations. After 8 nights, Wren will have read 30 pages: 2(8) + 14 = 16 + 14 = 30 After 8 nights, Jenni will have read 30 pages: 3(8) + 6 = 24 + 6 = 30

Solving Systems by Example 8 Graphing Video 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? Club A c = 3 r + 10 Club B c = 2 r + 15

Solving. Example Systems by Graphing 8 Continued Graph c = 3 r + 10 and c = 2 r + 15. 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.

Solving. Example Systems by Graphing 8 Continued Check (5, 25) using both equations. Number of movie rentals for Club A to reach $25: 3(5) + 10 = 15 + 10 = 25 Number of movie rentals for Club B to reach $25: 2(5) + 15 = 10 + 15 = 25

Lesson Wrap Solving Systems by Up Graphing Tell whether the ordered pair is a solution of the given system. Remember you do NOT have to graph the lines to answer these questions. 1. (– 3, 1); 2. (2, – 4); no yes

Solving Systems by Graphing Solve and CHECK the system by graphing. 3. y + 2 x = 9 y = 4 x – 3 (2, 5)
- Slides: 20