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System of Equations

System of Equations. Elimination Using addition and subtraction S. Calahan. Addition. Use elimination to solve the system of equations. 3x – 5y = -16 2x + 5y = 31 Since the coefficients of the y terms,

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System of Equations

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  1. System of Equations Elimination Using addition and subtraction S. Calahan

  2. Addition Use elimination to solve the system of equations. 3x – 5y = -16 2x + 5y = 31 Since the coefficients of the y terms, -5 and 5, are additive inverses, you can eliminate the y terms by adding the equations.

  3. ADD 3x – 5y = -16 + 2x + 5y = 31 5x = 15 We canceled the y terms leaving only the x terms on the left hand side.

  4. Now solve for x. 5x = 15 5 5 x = 3 Now let’s solve for y.

  5. Solve for y using substitution remember x = 3 3x – 5y = -16 2x + 5y = 31 Choose one of the original equations. 2x + 5y = 31 and replace the x with 3.

  6. Substitute and solve 2 (3) + 5y = 31 6 + 5y = 31 -6 -6 5y = 25 5 5 so, y = 5

  7. Since x = 3 and y = 5 The solution set for the equations 3x – 5y = -16 2x + 5y = 31 is (3,5). This set of equations has only one solution.

  8. Subtraction 5s + 2t = 6 9s + 2t = 22 Since the coefficients of the t terms, 2 and 2, are the same, you can eliminate the t terms by subtracting the equations.

  9. Add the opposite 5s + 2t = 6 -(9s + 2t = 22) becomes 5s + 2t = 6 -9s -2t = -22

  10. Now ADD 5s + 2t = 6 -9s - 2t = -22 - 4s = - 16 Cancel the 2t and the -2t

  11. Solve for s - 4s = - 16 - 4 - 4 s = 4 Now solve for t

  12. Substitute s = 4 into an original equation and solve for t 5s + 2t = 6 9s + 2t = 22 • Either equation will work. I will use 5s + 2t = 6 ,so 5(4) + 2y = 6

  13. 5s + 2t = 6 and s = 4 5(4) + 2t = 6 20 + 2t = 6 -20 = -20 2t = -14 2 2 , then t = -7.

  14. Therefore, the solution set for 5s + 2t = 6 9s + 2t = 22 is (4, -7).

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