1. Solving Systems – Choose Your Method
Objective: Solve systems of equations by choosing the most efficient method.

2. Methods for Solving Systems of Equations
Graphing Method
Used when equations are in slope-intercept form (y = mx + b) or standard form (Ax + By = C).
This can only be done by hand if the solution consists of whole numbers.
Substitution Method
Used when one of the equations is already solved for a variable or can be easily solved for one of the variables.
Elimination Method
Used when the order of like terms in the equations match.

3. Choose the Method
Which method would be the easiest to use to solve the following systems?
x – 2y = -6
x – y = 3
2y – x = 6
y = x – 3
y = x – 3
y = 1/2 x + 6
Elimination
Substitution
Graphing

4. Solving Systems of Equations
Solve the following system of equations:
y = -2x + 1
y = -x + 3
What is the best method to use?
Graphing
The solution to this system is (-2, 5).

5. Solving Systems of Equations
Solve the following system of equations:
3y + x = 6
y – 2x = -5
What is the best method to use?
Elimination
2( )
 6y + 2x = 12
6y + 2x = 12
y – 2x = -5
3y + x = 6
The solution to this system is (3, 1).
3(1) + x = 6
7y = 7
3 + x = 6
y = 1
x = 3

6. Solving Systems of Equations
Solve the following system of equations:
2x + y = 7
3x = 9
What is the best method to use?
Substitution
The solution to this system is (3, 1).
3x = 9
2x + y = 7
2(3) + y = 7
x = 3
6 + y = 7
y = 1

7. Solving Systems of Equations
Solve the following system of equations:
4y = 12 + x
x + y = -2
What is the best method to use?
Elimination
4y = 12 + x
-x + 4y = 12
x + y = -2
4y = 12 + x
The solution to this system is (-4, 2).
-x x
4(2) = 12 + x
-x + 4y = 12
5y = 10
8 = 12 + x
y = 2
-4 = x