3.2 Solving Linear Systems Algebraically
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1 3.2 Solving Linear Systems Algebraically Algebra III Mr. Niedert Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 1 / 10
2 Today s Learning Target(s) 1 I can solve a system of equations using substitution. 2 I can solve a system of equations using elimination. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 2 / 10
3 Using the Substitution Method When solving a linear system using substitution, use the following steps. The Substitution Method 1 Solve either equation for either of the variables. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 3 / 10
4 Using the Substitution Method When solving a linear system using substitution, use the following steps. The Substitution Method 1 Solve either equation for either of the variables. 2 Substitute the expression in for the variable you solved for in the equation you did not use in the previous step. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 3 / 10
5 Using the Substitution Method When solving a linear system using substitution, use the following steps. The Substitution Method 1 Solve either equation for either of the variables. 2 Substitute the expression in for the variable you solved for in the equation you did not use in the previous step. 3 Solve the equation for the variable in this new equation. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 3 / 10
6 Using the Substitution Method When solving a linear system using substitution, use the following steps. The Substitution Method 1 Solve either equation for either of the variables. 2 Substitute the expression in for the variable you solved for in the equation you did not use in the previous step. 3 Solve the equation for the variable in this new equation. 4 Substitute this value for the variable in either of the initial equations to find the last missing variable. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 3 / 10
7 The Substitution Method Example Solve the linear system below using substitution. { 3x y = 13 2x + 2y = 10 Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 4 / 10
8 The Substitution Method Practice Solve the linear system below using substitution. { x + 3y = 1 4x + 6y = 8 Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 5 / 10
9 Using the Elimination Method When solving a linear system using elimination, use the following steps. The Elimination Method 1 Multiply one or both of the equations by a constant to obtain coefficients that match, except for the fact that one is positive and one is negative. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 6 / 10
10 Using the Elimination Method When solving a linear system using elimination, use the following steps. The Elimination Method 1 Multiply one or both of the equations by a constant to obtain coefficients that match, except for the fact that one is positive and one is negative. 2 Add the two equations together. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 6 / 10
11 Using the Elimination Method When solving a linear system using elimination, use the following steps. The Elimination Method 1 Multiply one or both of the equations by a constant to obtain coefficients that match, except for the fact that one is positive and one is negative. 2 Add the two equations together. 3 Solve the result for one of the variables. If you have two variables at this step then you did not pick the correct values to multiply each equation by in Step 1. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 6 / 10
12 Using the Elimination Method When solving a linear system using elimination, use the following steps. The Elimination Method 1 Multiply one or both of the equations by a constant to obtain coefficients that match, except for the fact that one is positive and one is negative. 2 Add the two equations together. 3 Solve the result for one of the variables. If you have two variables at this step then you did not pick the correct values to multiply each equation by in Step 1. 4 Substitute this value for the variable in either of the initial equations to find the last missing variable. Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 6 / 10
13 The Elimination Method Example Solve the linear system below using elimination. { 2x 6y = 19 3x + 2y = 10 Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 7 / 10
14 The Elimination Method Practice Solve the linear system below using elimination. { 9x 5y = 7 6x + 4y = 2 Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 8 / 10
15 Using a Linear System as a Model Practice A citrus fruit company plans to make lb gift boxes of oranges and grapefruits. Each box is to have a retail value of $ Each orange weighs 0.50 lb and has a retail value of $0.75, while each grapefruit weighs 0.75 lb and has a retail value of $1.25. How many oranges and grapefruits should be included in the box? Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 9 / 10
16 3.2 Solving Linear Systems Algebraically Assignment pg #13, 16, 19, 22, 24, 26-27, 30, 33, 35-37, 54-55, 57 Algebra III 3.2 Solving Linear Systems Algebraically Mr. Niedert 10 / 10
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