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Solving Systems of Equations by Graphing

Learn how to solve systems of equations by graphing to determine if they have one solution, no solution, or infinite solutions. Understand the concept of systems of equations and graphing them to find the solutions in an easy and practical manner.

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Solving Systems of Equations by Graphing

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  1. Section 8.1 What we are Learning: To solve systems of equations by graphing Determine if a system of equations has one solution, no solutions, or infinite solutions by graphing

  2. System of Equations: • Two or more equations with two or more variables in them • They are used together to solve a problem • The solution to the system is an ordered pair which satisfies (answers) both equations • Ordered pair: (x, y), (s, t), (m, n)….

  3. Graphing a System of Equations: • Write each equation in slope-intercept form • Slope-intercept form: y = mx + b • b is the y-intercept; where the line crosses the y-axis • m is the slope • Example: • Carefully graph each equation • The point where the two equations cross is the ordered pair which is the solution to the System.

  4. Example:Graph the system of equations to find the solution. Now graph your lines! • 3x + 2y = 4 -2x + 8y = 16 • Rewrite each equation in slope intercept form. 3x + 2y = 4 -3x -3x 2y = -3x + 4 2 2 y = -3/2x + 2 -2x + 8y = 16 +2x +2x 8y = 2x + 16 8 8 y = 2/8x + 2 y = 1/4x + 2 Solution: (0, 2)

  5. If the Graphs of a System… • Intersect: • There is exactly one solution • Is called Consistent • Is called Independent • Are the Same Line: • There are infinitely many solutions • Is called Consistent • Is called Independent • Do Not Intersect are Parallel: • There is no solution • Is called Inconsistent

  6. Let’s Work This Together: • 2x + y = -4 5x + 3y = -6 Solution: Number of Solutions:

  7. Let’s Work This Together: • y = ¼ x + 7 4y = x Solution: Number of Solutions:

  8. Let’s Work This Together: • 4x + 2y = 8 3y = -6x + 24 Solution: Number of Solutions:

  9. Homework: • Page 459 • 27 to 37 odd Remember: Show all of your work and check your answers in the back of the book in order to receive credit!

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