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Solving Systems of Equations Using Elimination Method

This lesson focuses on the elimination method for solving systems of equations. Through a series of examples, students will learn to eliminate variables by addition or subtraction, simplifying their equations to find solutions. The lesson covers multiple examples where the x or y values are eliminated, guiding students through the processes of substitution and simplification. By the end, learners will be able to confidently solve equations in column form and interpret solutions through multiple-choice scenarios.

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Solving Systems of Equations Using Elimination Method

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Presentation Transcript

  1. Splash Screen

  2. Lesson 3 Contents Example 1Elimination Using Addition Example 2Write and Solve a System of Equations Example 3Elimination Using Subtraction Example 4Elimination Using Subtraction

  3. Use elimination to solve the system of equations. Write the equation in column form and add. Notice that the x value is eliminated. Divide each side by –2. Simplify. Example 3-1a Since the coefficients of the x terms, –3 and 3, are additive inverses, you can eliminate the x terms by addingthe equations.

  4. First equation Replace y with –15. Simplify. Add 60 to each side. Simplify. Divide each side by –3. Simplify. Example 3-1a Now substitute –15 for y in either equation to find the value of x. Answer: The solution is (–24, –15).

  5. Use elimination to solve the system of equations. Example 3-1b Answer: (2, 1)

  6. Four times one number three times another number minus is 12. – = 4x 3y 12 Two times the first number three times the second number added to is 6. + = 2x 3y 6 Example 3-2a Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. Let x represent the first number and y represent the secondnumber.

  7. Write the equation in column form and add. Notice that the y value is eliminated. Divide each side by 6. Simplify. Example 3-2a Use elimination to solve the system.

  8. First equation Replace x with 3. Simplify. Subtract 12 from each side. Simplify. Divide each side by –3. Simplify. Example 3-2a Now substitute3 for x in either equation to find the value of y. Answer: The numbers are 3 and 0.

  9. Example 3-2b Four times one number added to another number is –10. Three times the first number minus the second number is –11. Find the numbers. Answer: –3, 2

  10. Use elimination to solve the system of equations. Write the equation in column form and subtract. Notice that the x value is eliminated. Divide each side by 5. Simplify. Example 3-3a` ` Since the coefficients of the x terms, 4 and 4, are the same, you can eliminate the x terms by subtracting the equations.

  11. Second equation Simplify. Add 6 to each side. Simplify. Divide each side by 4. Simplify. Example 3-3a` ` Now substitute 2 for y in either equation to find the value of x. Answer: The solution is (6, 2).

  12. Use elimination to solve the system of equations. Example 3-3b Answer: The solution is (2, –6).

  13. Multiple-Choice Test Item If and what is the value of y?A(3, –8) B3C–8 D(–8, 3) Example 3-4a Read the Test Item You aregiven a system of equations, and you are asked to find the value of y.

  14. Write the equation in column form and subtract. Notice that the y value is eliminated. Divide each side by 14. Simplify. Example 3-4a Solve the Test Item You can eliminate the y terms by subtracting one equation from theother.

  15. First equation Simplify. Subtract 24 from each side. Simplify. Example 3-4a Now substitute 3 for x in either equation to solve for y. Notice that B is the value of x and A is the solution of the system of equations.However, the question asks for the value of y. Answer: C

  16. Multiple-Choice Test Item If and what is the value of x?A4B(4, –4)C(–4, 4) D–4 Example 3-4b Answer: D

  17. End of Lesson 3

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