L3-2 Obj: Solve a system by substitution and elimination

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L3-2 Obj: Solve a system by substitution and elimination Warm up Substitute 2y – 1 for x in each equation. Solve for y 1. x + 2y = 3 2. y – 2x = 8 3. 2y + 3x = -5 Substitute 2x + 5 for y in each equation and Solve for x 4. 2x – 2y = 4 5. 3x + y = 7

Steps for solving by substitution Choose one equation and solve for one of the variables Substitute the expression you found in step one into the other equation Solve Once you have found x or y, substitute that value into either equation to find the other variable

Steps for solving by elimination Make coefficient of x or y the same (one positive and one negative) Add the two equations Solve for the variable Substitute value of the variable you found in one of two original equations and solve for the other variable

Solve the system by substitution. Solving Systems Algebraically LESSON 3-2 Additional Examples x + 3y = 12 –2x + 4y = 9 Solve the system by substitution.

Ex 2: x + y = 10 x – y = 2

Ex 3: 4x - 3y = -2 4x + 5y = 14

Practice: 1. x – y = 0 x + y = 2 2. -x + 3y = -1 x - 2y = 2

Use the elimination method to solve the system. Solving Systems Algebraically LESSON 3-2 Additional Examples 3x + y = –9 –3x – 2y = 12 Use the elimination method to solve the system.

Solve the system by elimination. 2m + 4n = –4 3m + 5n = –3 Solving Systems Algebraically LESSON 3-2 Additional Examples Solve the system by elimination. 2m + 4n = –4 3m + 5n = –3

Solve each system by elimination. Solving Systems Algebraically LESSON 3-2 Additional Examples Solve each system by elimination. a. –3x + 5y = 6 6x – 10y = 0

(continued) b. –3x + 5y = 6 6x – 10y = –12 Solving Systems Algebraically LESSON 3-2 Additional Examples (continued) b. –3x + 5y = 6 6x – 10y = –12 A2_0302_QC.qtb

Practice Solve using elimination 1. 4x – 2y = 7 x + 2y = 3

2. 3x + 7y = 15 5x + 2y = -4

Solving Systems Algebraically LESSON 3-2 Additional Examples At Renaldi’s Pizza, a soda and two slices of the pizza-of-the-day costs $10.25. A soda and four slices of the pizza-of-the-day costs $18.75. Find the cost of each item.

Break-Even Point A theater production costs $40,000 plus $2800 per performance. A sold-out performance brings in $3675. How many sold-out performances will the production need to break even?

It costs $5,500,000 to build a ferry boat plus $15,000 in operating costs per trip. A sold-out trip brings in $24,000. How many sold-out trips will the ferry company need to break even? HW: L3-2 (p. 130) #4-8e 18-24e 30-40e 44-58e