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Section 8.1

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. System of Equations:. Two or more equations with two or more variables in them

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Section 8.1

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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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