Chapter 3 –Systems of Chapter 3 –Systems of Linear EquationsLinear Equations

3.2 – Solving Linear Systems 3.2 – Solving Linear Systems by Substitutionby Substitution

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

Today we will review:Today we will review:– Solving a system of linear equations in two Solving a system of linear equations in two

variables by substitutionvariables by substitution

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

Substitute (real-life) – Replace one Substitute (real-life) – Replace one thing with anotherthing with another

Substitute – Replace one variable with Substitute – Replace one variable with an expression containing the other an expression containing the other variablevariable

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

Steps for Solving a Linear System by Steps for Solving a Linear System by SubstitutionSubstitution– SolveSolve for one of the variables (the one with for one of the variables (the one with

no coefficient (number in front))no coefficient (number in front))– SubstituteSubstitute the value from the step 1 into the the value from the step 1 into the

other equation & solve for the other variableother equation & solve for the other variable– SubstituteSubstitute the value from step 2 into the the value from step 2 into the

revised equation from step 1 and solverevised equation from step 1 and solve– CheckCheck the solution the solution

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

Example 1Example 1– Solve the system using substitutionSolve the system using substitution

yy = 4 = 4xx

-2-2xx + + yy = -4 = -4

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

Example 2Example 2– Solve the system using substitutionSolve the system using substitution

33xx + 2 + 2yy = 1 = 1

-2-2xx + + yy = 4 = 4

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

Example 3Example 3– In one week, a pizza restaurant sold 210 In one week, a pizza restaurant sold 210

pizzas and made $2910. The price of a small pizzas and made $2910. The price of a small is $12 and the price of a large pizza is $15. is $12 and the price of a large pizza is $15. How many small pizzas and large pizzas were How many small pizzas and large pizzas were sold last week?sold last week?

3.2 – Solving Linear Systems by 3.2 – Solving Linear Systems by SubstitutionSubstitution

HOMEWORKHOMEWORK

Worksheet 3.2 Practice AWorksheet 3.2 Practice A