1. Solving for Variables
Section 1.6

2. What is the distance formula?
d = rt But what if we were given the distance and time, but wanted to find the rate? We need to isolate “r” r = d/t

3. What if we wanted to figure out Celsius given Fahrenheit:
The formula for a Fahrenheit temperature in terms of degrees Celsius is:
What if we wanted to figure out Celsius given Fahrenheit:
But remember you need multiply the whole left side by 5/9

4. Example: Solve for t s = 9s2 + t
Undo this as you would any other equation…what must you do to get t by itself?
s = 9s2 + t Subtract the 9s2 from both sides…
–9s –9s2
t = s – 9s2
This is the solution.

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

6. Example: Solve for b A = 5a2b
What must you do to get b by itself?
We must “undo” the multiplication by 5a2
A = 5a2b Divide 5a2 from both sides…
5a a2
b = A
5a2
This is the solution.

7. Solve for V: We can flip both sides of the equation!
Now just multiply both sides by “m”

8. Solve for m: We can flip both sides of the equation!
Now just multiply both sides by “m”

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

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

11. 3x – y = 12 -3x -3x -y = -3x + 12 y = 3x - 12 Solve for “y” -1 -1 -1
STUDENTS ALWAYS FORGET THE NEGATIVE!!! -1 -1 -1

12. Solve for “y”.
5x + 2y = 10
-5x x
2y = -5x + 10
y = x + 5 2 2 2

13. Solve for “y” 4(x – 3) + 3y = 12 4x – 12 + 3y = 12 -4x -4x
3y = -4x + 24
4(x – 3) + 3y = 12

14. Solve for “y” 2y + 3(y – 4) + 5x = 2 2y + 3y – 12 + 5x = 2
-5x -5x
5y - 12= -5x + 2
5y = -5x + 14
Solve for “y”
2y + 3(y – 4) + 5x = 2