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3.1 Solving Systems of Equations by Graphing

Learn to solve systems of equations by graphing, determine consistency, independence, or dependency. Examples provided with step-by-step instructions.

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3.1 Solving Systems of Equations by Graphing

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  1. 3.1 Solving Systems of Equations by Graphing Goals: ~Solve systems of equations by graphing ~Determine whether a system is consistent and independent, consistent and dependent, or inconsistent

  2. Terms • System of Equations:Two or more equations with the same variables • Consistent: Has at least 1 solution • Independent: Exactly one solution • Dependent: Infinite number of solutions • Inconsistent: No solution

  3. Consistent and Independent Inconsistent Consistent and Dependent Pictures

  4. Example 1: Solve by graphing • 2x+y = 5 x – y = 1 • Answer: Write each equation in slope-intercept form. • 2x+y=5 --> y=-2x+5 • x- y = 1 --> -y=-x+1 --> y=x-1 • Graph. (Graph y-int then follow the slope[rise/run] to get the next point) • The point where they cross is the solution

  5. Graph (2,1) is the solution.

  6. Example 2: Solve by graphing and describe as consistent and independent, cons. and dependent, or inconsistent

  7. Graph Solution is (2,1)

  8. Answer: • They cross only once, so the graphs are consistent and independent

  9. y = -x + 3 2y = -2x + 6 Solution : Put in slope-intercept form Graph using y-int and slope y = -x + 3 y = -x + 3 Example 2a: Without graphing, describe as consistent and independent, cons. and dependent, or inconsistent

  10. Answer • They both make the same graph, so they are consistent and dependent!!! 

  11. Without graphing, describe as consistent and independent, cons. and dependent, or inconsistent • 2a. y = 3x + 2 y = 3x -5 • 2b y = ½ x -6 y = 4x + 10

  12. Mr. Frazer bought 2 lbs of cheddar cheese and 3 lbs of turkey. He paid $26.35. Mrs. Cooper paid $18.35 for 1.5 lbs of cheese and 2 lbs of turkey. What was the price per pound of each item?

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