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# 3.2

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### 3.2

1. 1. CHAPTER 3 LINEAR SYSTEMS3.2 Solving Systems Algebraically Part 1: Substitution
2. 2. SYSTEM OF EQUATIONS A system of equations is a set of two or more equations A linear system consists of linear equations A solution of a system is a set of values for the variables that makes all the equations true. (usually an ordered pair)  Systems can be solved be various methods: graphing, substitution, and elimination
3. 3. SOLVING SYSTEMS BY SUBSTITUTION Use when it is easy to isolate one of the variables  At least one variable has a coefficient that is 1
4. 4. SOLVING SYSTEMSBY SUBSTITUTION1. Solve one equation for one of the variables2. Substitute the expression into the other equation and solve3. Substitute the solution into one of the original equations and solve for the remaining variable4. Check the solution
5. 5. SOLVING SYSTEMS BY SUBSTITUTION
6. 6. SOLVING SYSTEMS BY SUBSTITUTION
7. 7. SOLVING SYSTEMS BY SUBSTITUTION
8. 8. ASSIGNMENT 3.2 Substitution WS
9. 9. CHAPTER 3 LINEAR SYSTEMS3.2 Solving Systems Algebraically Part 2: Elimination
10. 10. SYSTEM OF EQUATIONS A system of equations is a set of two or more equations A linear system consists of linear equations A solution of a system is a set of values for the variables that makes all the equations true. (usually an ordered pair)  Systems can be solved be various methods: graphing, substitution, and elimination
11. 11. SOLVING BYELIMINATION1. Rewrite both equations in standard form2. Multiply one or both systems by an appropriate non-zero number (note you want one variable to drop out in the next step)3. Add the equations4. Solve for the variable5. Substitute the value into one of the original equation and solve for the remaining variable6. Check the solution
12. 12. SOLVE BY ELIMINATION
13. 13. SOLVE BY ELIMINATION
14. 14. SOLVE BY ELIMINATION
15. 15. SOLVING SYSTEMS WITHOUT UNIQUESOLUTIONS Solving a system algebraically can sometimes lead to infinitely many solutions and/or no solution  If you get a true result: infinitely many solutions  If you get a false result: no solution
16. 16. EXAMPLE: SOLVE THE SYSTEM
17. 17. EXAMPLE: SOLVE THE SYSTEM
18. 18. ASSIGNMENT 3.2 Elimination WS