Solving systems by substitution
- 1. 10.25.10 ACT Opener10.25.10 ACT Opener 1) Determine which ordered pair is a solution to the equation y = 4x + 6. A) (2, 3) B) (0, 4) C) (5, 26) D) (2, 8) E) (3, 12) 2) Determine which ordered pair is a solution to the system of equations. 2x – y = 8 and x + y = 1 F) (0, 0) G) (-2, 3) H) (2, 3) I) (-3, 2) J) (3, -2) 3) Solve the system by graphing. y = x y = 6 - x 4) Solve the system by graphing. Y = ½x + 1 4x – 8y = -8
- 2. Last Class….Last Class…. • Test Corrections – Due 10/29/10 • We learned to solve a system of equations using graphing. • There are several ways to solve a system of equations without using graphs.
- 3. The Substitution MethodThe Substitution Method 1. Solve one equation for one of the variables. – Get 1 variable in either equation by itself. 1. Substitute this expression in the other equation and solve for the other variable. 2. Substitute this value into equation from #1 and solve. 3. Write the solution as an ordered pair (x, y) 4. Check the values in both equations.
- 4. Example 1Example 1 Solve using substitution. y = 3x 2x + 4y = 28 2x + 4(3x) = 28 2x + 12x = 28 14x = 28 x = 2 y = 3(2) y = 6 (2,6) y = 3x
- 5. PracticePractice Solve using substitution. 1) x + y = 5 x = y + 1 2) a – b = 4 b = 2 – 5a
- 6. Example 2Example 2 Solve using substitution. 2x + y = 13 4x – 3y = 11 y = -2x + 13 4x – 3(-2x + 13) = 11 4x + 6x – 39 = 11 10x – 39 = 11 10x = 50 x = 5 2x + y = 13 2(5) + y = 13 10 + y = 13 y = 3 (5,3)
- 7. PracticePractice Solve using substitution. 1) x – 2y = 8 2x + y = 8 2) 3x + 4y = 2 2x – y = 5
- 8. Example 3Example 3 Solve using substitution. The sum of a number and twice another number is 13. The first number is 4 larger than the second number. What are the numbers? Let x = the first number Let y = the second number x + 2y = 13 x = y + 4 y + 4 + 2y = 13 3y + 4 = 13 3y = 9 y = 3 x = y + 4 x = 3 + 4 x = 7
- 9. PracticePractice Translate to a system of equations and solve. 1) The sum of two numbers is 84. One number is three times the other. Find the numbers.
- 10. PracticePractice Translate to a system of equations and solve. 1) The sum of two numbers is 84. One number is three times the other. Find the numbers.