1. 3.7 Solving for a Variable

2. Solve formulas for specified variables We are going to start dealing with equations with more than one variable. 3x + 2y = 6 This equation can be solved for either x or y. (We will be told which one to solve for). Here are other forumulasthat you may have seen before: P = 2L + 2W d = rt A = 1 bh 2 You can solve for any of the variables in any of these equations.

3. Example: Solve for tS = 9s 2 + t Undo this as you would any other equation…what must you do to get t by itself? S = 9s 2 + t Subtract the 9s 2 from both sides… –9s 2 –9s 2 t = S – 9s 2 Since S and s 2 are not like terms, they cannot be combined... This is the solution.

4. The formula for the Perimeter of a Rectangle is P = 2L + 2W Example: Solve for W P = 2L + 2W – 2L –2L P – 2L = 2W P – 2L = 2W 2 2 W= P – 2L 2 L W

5. Example: Solve for bA = 5a 2 b What must you do to get b by itself? We must “undo” the multiplication by 5a 2 A = 5a 2 b Divide 5a 2 from both sides… b =A 5a 2 This is the solution. 5a 2

6. -3 Solve for “y”. 5x – 3y = 6 -5x -5x -3y = -5x + 6 y = x - 2

7. 2y + 2 = 4x - 2 - 2 2y = 4x - 2 y = 2x - 1 Solve for “y” 222

8. Example: Solve for c How can you get c by itself? You could distribute the 1/2 h, but that would yield 2 fractions…...an easier way of handling this would be to multiply by the reciprocal of 1/2 first... Now, divide both sides by h... c = 2A – b h Subtract b from both sides... –b

9. Example: Solve for x One way to solve this is to multiply both sides by the common denominator of 2 and 8… Distribute the 4... x = 5s 3 Get x’s on one side, and s’s on the other... –x 3x – 4s = s +4s +4s 3x = 5s 4 3 8