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Algebra 2 3.2 Solving Linear Systems Algebraically Substitution and Elimination

Algebra 2 3.2 Solving Linear Systems Algebraically Substitution and Elimination. Learning Targets. Students should be able to… Use algebraic methods to solve linear systems (both substitution and elimination). Use linear systems to model real-life situations. Warm-up.

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Algebra 2 3.2 Solving Linear Systems Algebraically Substitution and Elimination

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  1. Algebra 2 3.2 Solving Linear Systems Algebraically Substitution and Elimination

  2. Learning Targets • Students should be able to… • Use algebraic methods to solve linear systems (both substitution and elimination). • Use linear systems to model real-life situations.

  3. Warm-up • Solve each equation for the indicated variable. • 2x – y = 5 Solve for y. • -x+2y = 3 Solve for x. • 3x – 4y = 12 Solve for y. • 3x – 4y = 12 Solve for x.

  4. Homework Check • 3.1 • Page 142 #12, 18, 41, 42, 43, 46, 49

  5. Review of Formulas • Slope Intercept Form: • Standard Form: • Point Slope Form: y = mx + b Ax + By = C

  6. Substitution • Steps to Solving a Linear Equation by Substitution: • Solve one of the equations for one of the variables • Substitute this expression into the other equation and solve for the remaining variable. • Take this value and substitute it into the equation you found from step 1 and solve for the remaining variable. • Check! (in original equations)

  7. Example 1: Solve the following systems using the substitution method. • 3x – y = 13 b. x + 3y = –2 2x + 2y = –10 –4x – 5y = 8

  8. c. x – y = 8 d. 2x – y = 14 –3x + 6y = –24 6x + 3y = 18

  9. Elimination/Linear Combination • Multiply one or both equations by a number so coefficients for 1 of the variables are opposite. • Add the equations eliminating one of the variables. Solve for the remaining variable. • Substitute this value into one of the original equations and solve for the other variable. • CHECK! (in original equations)

  10. Use Elimination to Solve • 3x – 5y = –36 2. 2x + 3y = –1 6x + 2y = 0 –5x + 5y = 15

  11. 6x + 2y = 20 4. 2x – 6y = 19 -4x + 3y = –22 –3x + 2y = 10

  12. Special Results 1. 6x – 4y = 14 2. 4x – 6y = 14 –3x + 2y = 7 –6x + 9y = –21

  13. Three ways to solve a system of linear equations: • 1. Graphing **Easy to graph – in slope intercept form or in an easy standard form • 2. Substitution **Easy to substitute – one of the variables has the coefficient of 1 or –1 • 3. Linear Combination (Elimination) **Easy to linear combine – coefficients in one equation is a multiple of the coefficient of the same variable in the other equation.

  14. Real World Problems 1. A citrus fruit company plans to make 13.25 lb gift boxes of oranges and grapefruits. Each box is to have a retail value of $21.00. Each orange weighs .5 lb and has a retail value of $.75, while each grapefruit weighs .75 lb and has a retail value of $1.25. How many oranges and grapefruits should be included in the box?

  15. Real World Problems 2. You are planting a 160 sq ft garden with shrubs and perennial plants. Each shrub costs $42 and requires 16 sq ft of space. Each perennial plant costs $6 and requires 8 sq ft of space. You plan to spend a total $270. How many of each type of plant should you buy to fill the garden?

  16. Closure

  17. Homework Assignment • 3.2 • Page 152 – 153 #substitution: 11, 18, elimination: 24, 34, any method: 35, 36, 39, 44, 47, 48

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