1.2.3 solving linear equations (multiple unknowns)
- 1. Unit 1: Algebraic Operations Chapter 2: Linear Equations and Formulae
- 2. Solving Equations 1.2.3 Solve a linear equation with multiple unknowns for any variable • Given a linear equation with more than one unknown, solve for the indicated variable Workbook p. 71 - 73
- 3. Solving Equations for Variables Example: Here we must get alone on one side of the equation. Some equations have more than one variable. We can solve an equation for one variable by rearranging the equation to get the variable alone on one side of the equation. Solve 3 10 forx y x x
- 4. To solve for a variable, follow these steps: Write the equation Move the variable you are solving for to the left side of the equation Move all other variables and numbers to the right side of the equation using the properties of equality. Solving Equations for Variables
- 5. Solving Equations for Variables Solve 3 10 forx y x 3 10x y 3 10x y 3 10 1 1 3 3 x y 1 3 10 3 y x Example: Write the equation: x is already on the left side of the equation Move y to the right side and change its sign. We need x alone, so multiply by to remove the 3. This is the answer, because x is alone on one side of the equation
- 6. Solving Equations for Variables 1 2 Example: Write the equation: is already on the left side of the equation Move to the right side and change its sign. We need alone, so multiply by to remove the 2. This is the answer, because is alone on one side of the equation Solve 2 3 21 fora b a 2 3 21a b a 2 1 32a b 3b 2 21 3 1 1 2 2 a b a 21 3 2 b a a
- 7. Solving Equations for Variables 5 Example: Write the equation: is already on the left side of the equation Move to the right side and change its sign. We need alone, so multiply by to remove the . This is the answer, because is alone on one side of the equation m 2 m m 1 Solve 2 6 for 5 m n m 1 2 6 5 m n 1 6 5 2m n 5 5 1 2 2 5 m n 10 10m n 1 5
- 8. Solving Equations for Variables 1 Example: Write the equation: is already on the left side of the equation Move to the right side and change its sign. We need alone, so multiply by to remove the negative. This is the answer, because is alone on one side of the equation b 3x b b Solve 3 forx b m b 3x b m 3xb m ( ) (( 3) ( ))1 1b m x 3 or 3 b m x b x m
- 9. Solving for Variables Checkpoint p. 72 Solve the equation 6 8 15 for pp q
- 10. Workbook p. 72 – 73 Solving for Variables