1. 3.2.1 – Linear Systems, Substitution

2. A system of linear equations is two or more equations, with two or more variables, that we need to solve for
We’ll generally stick with only two variables, x and y

3. Methods
There are various methods to use; some are more difficult than others, but we will have many options to use pending what case we have

4. Solutions
The solutions to the system of equations we deal with are the ordered pair (x, y)
The x and y we find MUST work for both equations

5. Example.
3x – y = 3
x + 2y = 8
The above is example of a system. What is different than the equations we have solved before?

6. Substitution The first method we will use is substitution
1) Pick an equation, and solve for one variable (try to pick the one which is easiest to solve for)
2) Substitute the expression you find into the other equation
3) Combine any like terms, distribute, etc., and solve for the remaining variable
4) Go back and find the other variable

7. Example. Solve the following system.
y = 2x
4x – y = 6
Is one variable already solved for?

9. Example. Solve the following system.
x – 2y = -3
3x + 2y = 7
Which variable is easiest to solve for?

11. Example. Solve the following system.
2x + y = 3
3x + y = 0

12. Now, try the following 3 problems with people around you
Now, try the following 3 problems with people around you. Write down your answers and we will check with other people.
1) m = 6n
2m – 4n = 16
2) x = y + 2
5x – 2y = 7
3) x = -y + 5
2x – y = 1

13. Assignment
Pg. 125
3-6, odd, 36