Solving Linear Systems with Substitution

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Solving Linear Systems with Substitution Section 3.2a 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Steps in Substitution SOLVE for one equation into one variable REPLACE one equation into other equation SUBSTITUTE the value into either equation CHECK the solution HINT: BEST TIME TO USE SUBSTITUTION IS WHEN AN EQUATION HAS AN ISOLATED VARIABLE 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 1 Solve using Substitution 1. SOLVE for one equation into one variable 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 1 Solve using Substitution 2. REPLACE one equation into other equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 1 Solve using Substitution 2. REPLACE one equation into other equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 1 Solve using Substitution 3. SUBSTITUTE the value into either equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 1 Solve using Substitution 3. SUBSTITUTE the value into either equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 1 Solve using Substitution 4. CHECK the solution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 2 Solve using Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Your Turn Solve using Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 3 Solve using Substitution 1. SOLVE for one equation into one variable 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 3 Solve using Substitution 2. REPLACE one equation into other equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 3 Solve using Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 3 Solve using Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 4 Solve using Substitution 1. SOLVE for one equation into one variable 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 4 Solve using Substitution 2. REPLACE one equation into other equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 4 Solve using Substitution 3. SUBSTITUTE the value into either equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 4 Solve using Substitution 3. SUBSTITUTE the value into either equation 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 4 Solve using Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Your Turn Solve using Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Application Steps Read the question, TWICE Understand and TRANSLATE the QUESTION Identify all variables by appropriately LABELING (this is required) SOLVE using Substitution or Elimination and label accordingly CHECK answer 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

How much of each type of coffee is in 50 lb of the blend? Example 5 A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend? How much of each type of coffee is in 50 lb of the blend? Let x represent the amount of the Sumatra beans in the blend. Let y represent the amount of the Kona beans in the blend. 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

Amount of Sumatra beans Example 5 A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend? Write one equation based on the amount of each bean: Amount of Sumatra beans plus amount of Kona beans equals x y 50. 50 + = Write another equation based on cost of the beans: Cost of Sumatra beans plus cost of Kona beans equals 5x 13y cost of beans. 10(50) + = 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 5 A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend? Solve the system. 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Example 5 A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend? Solve the system. The mixture will contain 18.75 lb of the Sumatra beans and 31.25 lb of the Kona beans. 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution

3.2a - Solving Systems through Substitution Assignment WKST Substitution 11/19/2018 7:51 AM 3.2a - Solving Systems through Substitution