3 2 SOLVING LINEAR SYSTEMS ALGEBRAICALLY Algebra 2

3. 2 SOLVING LINEAR SYSTEMS ALGEBRAICALLY Algebra 2

Substitution 1) 2) 3) v Solve one of the equations for one of its variables Substitute the expression from step 1 into the other equations and solve for the other variable Substitute the value from step 2 into the revised equation from step 1 and solve Used only when there is a single variable

Examples

Linear Combinations (Elimination) 1) 2) 3) Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. Add the revised equations for step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.

Examples

Examples

Examples:

Example 6) 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 0. 50 lb and has a retail value of $. 75, while each grapefruit weighs 0. 75 lb and has a retail value of $1. 25. How man oranges and grapefruits should be included in the box?

Example 7) You are planting a 160 ft 2 garden with shrubs and perennial plants. Each shrub costs $42 and requires 16 ft 2 of space. Each perennial plant costs $6 and requires 8 ft 2 of space. You plan to spend a total of $270. How many of each type of plant should you buy to fill the garden?