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Math Pacing

Elimination Using Addition and Subtraction. Math Pacing. The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers?

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Math Pacing

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  1. Elimination Using Addition and Subtraction Math Pacing • The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers? • Complementary angles have a sum of 90°. Angles A and B are complementary and the measure of angle A is 14 ° less than the measure of angle B. Find the measures of angles A and B. • What value of c in the system of equations 5x + y = – 1 and – 2y = 10x + c will produce a system of equations with infinitely many solutions? Let x = the greater number Let y = the lesser number Let x = the measure of A Let y = the measure of B

  2. Elimination Using Addition and Subtraction Elimination Using Addition and Subtraction

  3. Elimination Using Addition and Subtraction Sometimes adding two equations together will eliminate one variable. Using this step to solve a system of equations is called elimination. Elimination Using Addition and Subtraction

  4. 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. Elimination Using Addition 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.

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

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

  7. 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 Write and Solve a System of Equations 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.

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

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

  10. Write and Solve a System of Equations 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

  11. Elimination Using Addition and Subtraction Elimination Using Addition and Subtraction Sometimes subtracting one equation from another will eliminate one variable.

  12. 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. Elimination Using Subtraction 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.

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

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

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

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

  17. First equation Simplify. Subtract 24 from each side. Simplify. Elimination Using Subtraction 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

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

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