3.1 Solving Linear Systems by Graphing 9/20/13

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. Vocabulary System of 2 Linear Equations: A system consisting of two linear equations in two variables. Ex: 6x – 2y = 8 3x – y = 4

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 4(3) – 2(4) = 3 12 – 8 = 3 Answer: Not a 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 (4) = = 11 2(3) – 4 = 2 6 – 4 = 2 Answer: Solution

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

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

Add or subtract the x – term on both sides of the equation. Divide everything by the coefficient of y if the coefficient is not 1.

Example 2 ANSWER () 2, 3 Solve a System by Graphing Solve the system by graphing. Then check your solution algebraically. 33x3x–y = 8x+2y2y = In slope int. form: y = 3x - 3

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 1Equation 2 33x3x–y = 8x+ 2y2y = () 233–3 = ? 28 + = ? () 32 36–3 = ? 28 + = ? 6 33 = 88 = ANSWER ( ).). 2, 3 The solution of the system is

Extra Example 2. x3y3y = – 1 xy = + 1 –– ANSWER () 1, 0 Solve the system by graphing. Then check your solution.

Checkpoint ANSWER () 2, 1 Solve a System by Graphing Solve the system by graphing. Then check your solution.

Homework WS 3.1. Do all work on the worksheet. Pencil only. Use straight edge/Ruler

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)

Systems with Many or No Solutions Example 3 Tell how many solutions the linear system has. a. 1 = y – 2x2x+ = 2y2y – 4x4x2 – b. + = 2y2yx1 + = 2y2yx4 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 without graphing. Checkpoint ANSWER 0 Write and Use Linear Systems 2. 5 = 4y4y – x + = 4y4y – x5 – 1. + = 3y3y2x2x1 + = 6y6y4x4x3 ANSWER infinitely many solutions ANSWER = 5y5y – x + = 5y5yx 5