Tuesday December 10, 2013Bell Ringer:

Solve the following equation:

4(a - 6) + 4 = 2a - 6

What We are Learning Today:

• To solve systems of equations using substitution

Substitution:

• From our Properties of Real Numbers:• If a = b,

• “a” may be replaced by “b”Example: Evaluate 6x – 7 if x = 3

How do we Solve a System of Equations Using Substitution?

• If the equations are already written in terms of x or y:1. Choose the equation solved for a variable

2. Substitute the x or y value (what is on the right side of the =) into the other equation for that variable

3. Solve for the second variable.

4. Substitute answer back into one of the original equations to solve for the second variable.

We Will Have:

• One Solution• x = a number different than y’s number• y = a number different than x’s number

• Infinite Solutions• A number = same number

• No Solution• A number ≠ another number

Example:Using Substitution Solve y = 4x – 13 y = 12x + 3

• Step 1: • Step 2:

4x – 13 = 12x + 3

-4x -4x

-13 = 8x + 3

-3 -3

-16 = 8x

8 8

-2 = x

y = 4x – 13

y = 4(-2) – 13

y = -8 – 13

y = -21

OR

y = 12x + 3

y = 12(-2) + 3

y = -24 + 3

y = -21

Solution: (-2, -21)

Let’s Work This Together:

2x + 7y = 3

x = 1 – 4y

Let’s Work This Together:

y = -3x + 8

y = -4 + x

Let’s Work This Together:

8x + 2y = 13

y = -4x + 11

Let’s Work This Together:

6x – 2y = -4

y = 3x + 2

Practice Time:

• Solve by Substitution Worksheet #1• Show ALL work for each equation• Write the solution as an ordered pair• If there is not a solution state whether

there is infinitely many or no solutions