3.1 Solving Linear Systems by Graphing 10/1/12

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.

Tell whether the ordered pair (3, 4) is a solution of -2x + y = -2 4x – 2y = 3 Substitute 3 for x and 4 for y in BOTH equations. -2(3) + 4 = -2 - 6 + 4 = -2 4(3) – 2(4) = 3 12 – 8 = 3 Answer: Not a Solution

Answer: Solution Tell whether the ordered pair (3, 4) is a solution of x + 2y = 11 2x – y = 2 Substitute 3 for x and 4 for y in BOTH equations. 3 + 2(4) = 11 3 + 8 = 11 2(3) – 4 = 2 6 – 4 = 2 Answer: Solution

Solve the system by graphing. Then check your solution. Example 1 Solve a System by Graphing Solve the system by graphing. Then check your solution. 3 y – x = + 9 y 2 x = + ANSWER ( ) 2, 5 –

y = - x + 3 5= -(-2) + 3 5= 5 y = 2 x + 9 5 = 2(-2) + 9 5 = -4 + 9 You can check the solution by substituting -2 for x and 5 for y into the original equations. y = - x + 3 5= -(-2) + 3 5= 5 y = 2 x + 9 5 = 2(-2) + 9 5 = -4 + 9 5 = 5

Solve the system by graphing. Then check your solution algebraically. Example 2 Solve a System by Graphing Solve the system by graphing. Then check your solution algebraically. 3 3x – y = In slope int. form: y = 3x - 3 8 x + 2y = ANSWER ( ) 2, 3 In slope int. form: y = - 1 2 x + 4

The solution of the system is Example 2 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 3 3x – y = 8 x + 2y ( ) 2 3 – = ? 8 + 3 6 – = ? 2 8 + 3 = 8 ANSWER ( ). 2, 3 The solution of the system is 8

Extra Example Solve the system by graphing. Then check your solution. 1. x 3y = – 1 x y = + 1 – ANSWER ( ) 1, 0

Solve the system by graphing. Then check your solution. Checkpoint Solve a System by Graphing Solve the system by graphing. Then check your solution. 2. 2 + 4y x – = 2x 3y = – 6 ANSWER ( ) 6, 2

Homework WS 3.1

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)

Tell how many solutions the linear system has. Example 3 Systems with Many or No Solutions Tell how many solutions the linear system has. b. + = 2y x 1 4 a. 1 = y – 2x + = 2y – 4x 2 Infinitely many solutions :the lines have the same equation. No solution :the lines are parallel (same slope)

Tell how many solutions the linear system has. Checkpoint Write and Use Linear Systems Tell how many solutions the linear system has. 3. + = 3y 2x 1 6y 4x 3 ANSWER 4. 5 = 4y – x + ANSWER infinitely many solutions 5. 5 = 5y – x + ANSWER 1