1. Chapter 7 – Solving Systems of Linear Equations 7.3 – Solving Linear Systems by Linear Combinations

2.  Today we will be learning how to: Use linear combinations to solve a system of linear equations Model a real-life problem using a system of linear equations

3. 7.3 – Solving Linear Systems by Linear Combinations  Example 1 Solve the linear system.  -x + 2y = -8  x + 6y = -16

4. 7.3 – Solving Linear Systems by Linear Combinations  A linear combination of two equations is an equation obtained by adding one of the equations (or a multiple of that equation) to the other equation (or a multiple of that equation).

5. 7.3 – Solving Linear Systems by Linear Combinations  Example 2 Solve the linear system.  5x – 4y =3  2x + 8y = -2

6. 7.3 – Solving Linear Systems by Linear Combinations  Example 3 Solve the linear system.  3x = -6y + 12  -x + 3y = 6

7. 7.3 – Solving Linear Systems by Linear Combinations  STEPS FOR SOLVING A LINEAR SYSTEM BY LINEAR COMBINATIONS 1. 2. 3. 4.

8. 7.3 – Solving Linear Systems by Linear Combinations  Example 4 Solve the linear system.  11x + 3y = 1  -5x – 3y = -7

9. 7.3 – Solving Linear Systems by Linear Combinations  Example 5 Solve the linear system.  2u = 4v + 8  3v = 5u – 13

10. 7.3 – Solving Linear Systems by Linear Combinations HOMEWORK Page 414 #8 – 24 even