Solving Equations Solving Equations and Formulasand Formulas

Chapter 2 section 6Chapter 2 section 6

Solving for a specific Solving for a specific VariableVariable

Sometimes Sometimes equations involve equations involve multiple multiple variables, or variables, or letters that stand letters that stand for specific for specific things, such as things, such as scientific scientific formulas and formulas and physics equationsphysics equations

Geometry Formulas:Geometry Formulas:

The formula for The formula for Circumference of a Circumference of a circle is:circle is:

C=2πr (2 x pi x radius)

We can solve the formula for r: (this means get r by itself!)

What do you think we could What do you think we could do?do?

If the equation is set up as If the equation is set up as C = 2πr, and you are asked to get r by itself, then you need to first ask yourself: What is attached to r? How can you “undo” the operation?

Since 2π is “stuck” to r by multiplication, you could get rid of it by division……

Example 1 - Like this!Example 1 - Like this!

C =2πr Divide both sides by 2π: 2π 2π This leaves you with the following:

C = r2π

That’s it! That is all there is to it! Now r is by itself, and all of the other “stuff” is on

the other side!

Ex. 2 Here’s another Ex. 2 Here’s another one:one:

Try solving the following formula for y:Try solving the following formula for y:

12x + 3y = 612x + 3y = 6

Follow these steps to get Follow these steps to get y:y:

12x + 3y = 612x + 3y = 61.1. Move your x’s to the right side of the equal signMove your x’s to the right side of the equal sign

12x +3y = 612x +3y = 6 - 12x -12x- 12x -12x

3y = -12x + 63y = -12x + 6-12x and 6 are not like terms so you can’t combine -12x and 6 are not like terms so you can’t combine

them.them.

Steps 2 & 3:Steps 2 & 3:

Now your equation should look like this!Now your equation should look like this!

3y = -12x + 63y = -12x + 6

2. What would be the next thing you should do to get the y by 2. What would be the next thing you should do to get the y by itself? itself?

(If you said DIVIDE BY 3, THEN YOU ARE RIGHT!)(If you said DIVIDE BY 3, THEN YOU ARE RIGHT!)

3Y3Y = = -12x -12x ++ 6 6 3 3 3 3 3 3

3. Your answer will be 3. Your answer will be y = -4x + 2 y = -4x + 2

Ex. 3 How ‘bout Ex. 3 How ‘bout another one?!?another one?!?

Solve 6 – ay = 4(a – b) for the variable in red

Just follow the steps you have Just follow the steps you have been using in other types of been using in other types of

equations!equations! 6 – ay = 4(a – b) Distributive property:

6 – ay = 4a – 4b Get the things with an “b” alone on one side of

the equal sign

6 – ay = 4a – 4b - 4a - 4a Simplify to get:

6 – ay – 4a = - 4b

Big Finish:Big Finish:

6 – ay – 4a = - 4b -4 -46 – ay – 4a = b -4

Divide both sides by -4 to solve for b

Ex. 4 Try one more :Ex. 4 Try one more :(if your brain is not already (if your brain is not already

fried!)fried!) The perimeter of a square field is

given by the equation P = 2l + 2w, where P represents the

perimeter, l represents the length of the field, and w represents the width of the field.

Solve the formula for l.

What should you do first?What should you do first?

Answer:Answer: P = 2l + 2w - 2w - 2w

P - 2w = 2l 2 2 P - 2w = l 2

OMG!!!!OMG!!!! Yes, these are hard!Yes, these are hard! Yes, you have to do them!Yes, you have to do them! Yes, you have an Yes, you have an

assignment!assignment! Book page 113 2 – 26 evenBook page 113 2 – 26 even

(13 problems)(13 problems)

You’ll thank me one You’ll thank me one day…….day…….