3.2 Solving Linear Systems Algebraically
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This document provides examples of solving systems of linear equations using substitution and combination methods. It demonstrates solving 3x+4y=-4 and x+2y=2 by substitution, solving -x+3y=1 and 4x+6y=8 by substitution, and solving 2x-4y=13 and 4x-5y=8 by combination. It also shows multiplying equations by constants before combining, and solving a 4 equation system.
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3.2 Solving Linear Systems Algebraically
- 2. Example: 1. Solve one equation for one variable. 3x + 4y = -4 x + 2y = 2 2. Substitute that into the other equation and solve. 3. Plug in that answer and solve for the other variable.
- 3. Solve the linear system using substitution. 3x – y = 13 2x + 2y = -10
- 4. Solve the linear system using substitution. -x + 3y = 1 4x + 6y = 8
- 5. Example: 1. Multiply one or both equations by a 2x – 4y = 13 constant. 4x – 5y = 8 2. Add the two equations to eliminate a variable. Solve for the other. 3. Plug in that solution to solve for the other variable.
- 6. Solve the system using combination. 2x – 6y = 19 -3x + 2y = 10
- 7. Solve the system using combination. 3x + 2y = 6 -6x - 3y = -6
- 8. We can multiply both equations by a different number! Solve the system. 7x - 12y = -22 -5x + 8y = 14
- 9. Solve the system using combination. 9x – 5y = -7 -6x + 4y = 2
- 10. Solve the linear system. x – 2y = 3 6x – 10y = 12 2x – 4y = 7 -15x + 25y = -30