Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

no text concepts found

Transcript

1.1 Solving Linear Systems by Graphing 9/14/12 Vocabulary System of 2 Linear Equations: A system consisting of two linear equations in two variables. Ex: 6x – 2y = 8 3x – y = 4 Solution of a system of 2 linear equations: Is an ordered pair (x, y) that satisfies both equations. Graphically, it’s the point where the lines intersect. Example 1 Solve a System by Graphing Solve the system by graphing. Then check your solution algebraically. Equation 1 3x – y = 3 ANSWER Equation 2 x + 2y = 8 ( 2, 3 ) Example 1 Solve a System by Graphing You can check the solution by substituting 2 for x and 3 for y into the original equations. Equation 1 Equation 2 3x – y = 3 x + 2y = 8 3( 2) – 3 =? 3 ? 8 2 + 2( 3) = ? 3 6 – 3= ? 8 2 +6 = 3=3 8=8 ANSWER The solution of the system is ( 2, 3 ). Solve a System by Graphing Checkpoint Solve the system by graphing. Then check your solution. 1. y = – x + 3 y = 2x + 9 ANSWER ( –2, 5 ) Solve a System by Graphing Checkpoint Solve the system by graphing. Then check your solution. 2. x – 3y = 1 –x + y = – 1 ANSWER ( 1, 0 ) Solve a System by Graphing Checkpoint Solve the system by graphing. Then check your solution. 3. – x + 4y = 2 2x – 3y = 6 ANSWER ( 6, 2 ) Number of Solutions 1 solution : the lines have different slopes Infinitely many solutions :the lines have the same equation. No solution :the lines are parallel (same slope) Homework 1.1 #1, 3, 5, 7-14

Related documents