Solving Linear Equations with One or Two Variables A linear equation is an equation that can be written in the form of Ax + B = C , where A , B...
Solving Linear Equations with One or Two Variables
A linear equation is an equation that can be written in the form of Ax + B = C, where A, B, and C are constants and x is the variable.
Step 1: Identify the coefficients of the variables.
The coefficients are the numbers next to the variable in each term of the equation.
A: The coefficient of x in the equation.
B: The coefficient of the y variable.
C: The constant term.
Step 2: Solve for the variable.
There are two main methods for solving linear equations:
Method 1: Using inverse operations
Start by isolating the variable on one side of the equation using inverse operations (e.g., adding, subtracting, multiplying, dividing).
Method 2: Using equality properties
Apply properties of equality (e.g., addition/subtraction, multiplication/division) to simplify both sides of the equation.
Step 3: Check your solution.
Substitute the value of x you found into the original equation to see if it produces the original equation's solution.
Example:
Solve the equation:
2x + 5 = 13
Solution:
A: A = 2
B: B = 5
C: C = 13
Using Method 1, we isolate x:
2x = 8
Solution: x = 4
Verification:
Substituting x = 4 back into the original equation, we get:
2(4) + 5 = 13
True
Tips for Solving Linear Equations:
A linear equation will always have one variable and one constant term.
The goal is to isolate the variable on one side of the equation using inverse operations.
Pay attention to the signs of the coefficients and the constant term when solving.
Check your solutions by substituting them back into the original equation to ensure they produce the expected results