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8.2 Solving by Substitution

8.2 Solving by Substitution. Objective: To solve a system of equations by substituting for a variable. -3. -3. Solving by Substitution. When one variable is alone on one side of the equation, you can substitute for that variable in the other equation. x + y = 13. x = y + 3.

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8.2 Solving by Substitution

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  1. 8.2 Solving by Substitution • Objective: To solve a system of equations by substituting for a variable

  2. -3 -3 Solving by Substitution • When one variable is alone on one side of the equation, you can substitute for that variable in the other equation. x + y = 13 x = y + 3 (y + 3) + y = 13 x = 5 + 3 2y + 3 = 13 x = 8 2y = 10 (8, 5) y = 5

  3. Solving by Substitution y = 3x 3x 2x + 4y = 28 y = 3( ) 2x + 4() = 28 2x + 12x = 28 y = 6 14x = 28 (2, 6) x = 2 2

  4. -2 -2 (1, 7) Solving by Substitution x + y = 8 y = 2 + 5x x + (2 + 5x)= 8 y = 2 + 5(1) 6x + 2 = 8 y = 7 6x = 6 x = 1

  5. -x -x Solving by Substitution y = x + 2 3 y = 2x - 1 y = 5 x + 2 = 2x - 1 2 = x - 1 (3, 5) 3 = x

  6. Solve for X Solve for y

  7. Parenthesis!!! -y -y (4, 1) Solving by Substitution x + y = 5 2x + 3y = 11 x = 5 - y 1 2(5 – y) + 3y = 11 x = 4 10 – 2y + 3y = 11 10 + y = 11 y = 1

  8. -39 -39 -2x -2x (5, 3) Solving by Substitution 2x + y = 13 8x + 3y = 49 8x + 3( y )= 49 13 -2x y = 13 – 2x 8x + 39 - 6x = 49 2x + 39 = 49 y = 13 – 2( x ) 5 2x = 10 y = 3 x = 5

  9. The sum of two numbers is 82. One number is 12 more than the other. What are the numbers? Let x = the larger number and y the smaller.

  10. The difference between two numbers is 9. Three times the larger number is six times the smaller. What are the numbers?

  11. Homework tonight: • Page 365 (2-26) even

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