Methods for Solving and Graphing
Linear Equations
1. Elimination Method (Systems of Equations)
Idea: Add or subtract equations to eliminate one variable.
Steps:
1. Align both equations in standard form (Ax + By = C)
2. Multiply if needed to make one variable have opposite coefficients
3. Add or subtract equations
4. Solve for the remaining variable
5. Substitute back to find the other variable
Example:
x + y = 10
x-y=2
Add both equations:
2x = 12 → x = 6
Substitute:
6 + y = 10 → y = 4
Solution: (6, 4)
2. Substitution Method
Idea: Solve one equation for one variable, then substitute into the other.
Steps:
1. Solve one equation for x or y
2. Substitute into the second equation
3. Solve
4. Substitute back to find the other variable
Example:
y=x+1
x+y=9
Substitute:
x + (x + 1) = 9
2x + 1 = 9 → 2x = 8 → x = 4
Linear Equations
1. Elimination Method (Systems of Equations)
Idea: Add or subtract equations to eliminate one variable.
Steps:
1. Align both equations in standard form (Ax + By = C)
2. Multiply if needed to make one variable have opposite coefficients
3. Add or subtract equations
4. Solve for the remaining variable
5. Substitute back to find the other variable
Example:
x + y = 10
x-y=2
Add both equations:
2x = 12 → x = 6
Substitute:
6 + y = 10 → y = 4
Solution: (6, 4)
2. Substitution Method
Idea: Solve one equation for one variable, then substitute into the other.
Steps:
1. Solve one equation for x or y
2. Substitute into the second equation
3. Solve
4. Substitute back to find the other variable
Example:
y=x+1
x+y=9
Substitute:
x + (x + 1) = 9
2x + 1 = 9 → 2x = 8 → x = 4
