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3.1 Solving Linear Systems by Graphing

3.1 Solving Linear Systems by Graphing. 9/20/13. 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:.

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3.1 Solving Linear Systems by Graphing

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  1. 3.1 Solving Linear Systems by Graphing 9/20/13

  2. 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.

  3. 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

  4. 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

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

  6. You can check the solution by substituting -2for x and 5for 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

  7. Standard  Slope Int Form • 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. Ex. Ex.

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

  9. Example 2 ? ? = = Equation 1 Equation 2 ( 2, 3 ). = x + 8 2y ? 2 8 2 + 3 – 3 3 = The solution of the system is ? 6 – 3 3 6 = 2 8 + = 3x – y 3 = = 3 8 3 8 ANSWER ( ( ) ) 2 3 Solve a System by Graphing You can check the solution by substituting 2 for x and 3 for y into the original equations.

  10. Extra Example – – + – = x y 1 = x 3y 1 ANSWER ( 1, 0 ) Solve the system by graphing. Then check your solution. 2.

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

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

  13. Number of Solutions 1 solution : the lines have different slopes No solution :the lines are parallel (same slope) Infinitely many solutions :the lines have the same equation.

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

  15. Checkpoint 3. 1. 2x + 3y 1 = 0 ANSWER 4x + 6y 3 = 1 ANSWER 2. – x 4y 5 = – – x + 4y 5 = infinitely many solutions ANSWER – x 5y 5 = x + 5y 5 = Write and Use Linear Systems Tell how many solutions the linear system has without graphing.

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