1 / 16

210 likes | 396 Views

A system of equations is a set of two or more equations that are to be solved. A solution of a system of two equations in two variables is an ordered pair of numbers that makes both equations true. A solution to two equations (1, 3) for y = 2x + 1 and y = 5x - 2. –3 x –3 x.

Download Presentation
## A system of equations is a set of two or more equations that are to be solved.

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**A system of equations is a set of two or more equations that**are to be solved.**A solutionof a system of two equations in two variables is**an ordered pair of numbers that makes both equations true. A solution to two equations (1, 3) for y = 2x + 1 and y = 5x - 2**–3x –3x**Example 1: Solving Systems of Linear Equations by Graphing y = 2x – 7 3x + y = 3 Step 1: Solve both equations for y. 3x + y = 3 y = 2x – 7 y = 3 – 3x Step 2: Graph. The lines intersect at (2, –3), so the solution is (2, –3).**?**? –3 = 2(2)– 7 3(2) + (–3) = 3 ? ? –3 = –3 3 = 3 Example 1A Continued Check y = 2x – 7 3x + y = 3**Not all systems of linear equations have graphs that**intersect in one point. There are three possibilities for the graph of a system of two linear equations, and each represents a different solution set.**+ 9+9**–2x –2x Example 2: Solving Systems of Linear Equations by Graphing 2x + y = 9 y – 9 = –2x Step 1: Solve both equations for y. 2x + y = 9 y – 9 = –2x y = –2x + 9 y = –2x + 9 Step 2: Graph. The lines are the same, so the system has infinitely many solutions.**?**y = y ? –2x + 9 = –2x + 9 +2x +2x ? 9 = 9 Example 1B Continued Check**–5x –5x**Example 3 y = –4x + 1 5x + y = –1 Step 1: Solve both equations for y. y = –4x + 1 5x + y = –1 y = –5x – 1 Step 2: Graph. The lines are intersect at (–2, 9), so the solution is (–2, 9).**?**? 9 = –4(–2)+ 1 5(–2) + (9) = –1 ? ? 9 = 9 –1 = –1 Example 3 Continued Check y = –4x + 1 5x + y = –1**Application: Example 1**A bus leaves the school traveling west at 50 miles per hour. After it travels 15 miles, a car follows the bus, traveling at 55 miles per hour. After how many hours will the car catch up with the bus? Let t = time in hours Let d = distance in miles bus distance: d = 50t + 15 car distance: d = 55t**?**165 = 50(3) + 15 ? 165 = 55(3) Application: Example 1 Continued Graph each equation. The point of intersection appears to be (3, 165). Check d = 50t + 15 200 150 Distance (mi) 100 165 = 165 50 d = 55t 1 2 3 4 5 6 7 8 9 10 Time (h) 165 = 165 The car will catch up after 3 hours, 165 miles from the school.**Lesson Quiz**Solve each system of equations by graphing. Check your answer. 1. A car left Cincinnati traveling 55 mi/h. After it had driven 225 miles, a second car left Cincinnati on the same route traveling 70 mi/h. How long after the 2nd car leaves will it reach the first car? 15 h 2.y = x; y = 3x (0, 0) 3.y = 4 – x; x + y = 1 no solution**Lesson Quiz for Student Response Systems**1. Solve the system of equations. y = 2 – x 2y = 4 – 2x A. no solution B. infinitely many solutions C. (1, 1) D. (2, 2)**Lesson Quiz for Student Response Systems**2. Solve the system of equations. y = 5 – x 3 – x = y A. no solution B. infinitely many solutions C. (3, 5) D. (5, 3)**Lesson Quiz for Student Response Systems**3. Solve the system of equations. y = 5 – 2x 3x = y A. no solution B. infinitely many solutions C. (1, 3) D. (3, 1)

More Related