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January 11, 2016 7.3 Solving Linear Systems of Equations Take 3: Elimination Method Addition/Subtraction w/ Multiplication Can we solve both of these systems with elimination? x - 3y = -4 x + 4y = 20 -x - 2y = -1 2x - y = 16 January 11, 2016 x + 4y = 20 2x - y = 16 Solving Systems by Elimination 1. Rewrite system to align like terms 2. Multiply one (or both) equation(s) so that one of the variables can be eliminated 3. Eliminate 1 of the variables 4. Solve for other variable 5. Plug it back into original equation January 11, 2016 Solving Systems by Elimination Example #1 x + 4y = 20 2x - y = 16 1. Rewrite system to align like terms 2. Multiply one (or both) equation(s) so that one of the variables can be eliminated x + 4y = 20 4(2x - y = 4) x + 4y = 20 8x - 4y = 16 3. Eliminate 1 of the variables 9x = 36 4. Solve for other variable x=4 5. Plug it back into original equation x + 4y = 20 4 + 4y = 20 4y = 16 y=4 6. Check January 11, 2016 1. Rewrite to align like terms Example # 2: 4x + y = 8 x - 7y = 2 2. Multiply 3. Eliminate a variable 4. Solve 5. Plug it in 6. Check January 11, 2016 1. Rewrite to align like terms Example # 3: 2x + 5y = 3 -x + 3y = -7 2. Multiply 3. Eliminate a variable 4. Solve 5. Plug it in 6. Check January 11, 2016 1. Rewrite to align like terms Example # 4: 5x + 3y = 2 2x = -y 2. Multiply 3. Eliminate a variable 4. Solve 5. Plug it in 6. Check January 11, 2016 1. Rewrite to align like terms Example # 5: 5x + 3y = 12 4x - 5y = 17 2. Multiply 3. Eliminate a variable 4. Solve 5. Plug it in 6. Check January 11, 2016 January 11, 2016 7.3 Solving Linear Systems of Equations Take 3: Elimination Method Addition/Subtraction w/ Multiplication Can we solve both of these systems with elimination? x - 3y = -4 x + 4y = 20 -x - 2y = -1 2x - y = 16 January 11, 2016