Solving Linear Equations with Two or Three Variables A linear equation with two or three variables can be represented in the form of: Ax + By + C = D wh...
Solving Linear Equations with Two or Three Variables
A linear equation with two or three variables can be represented in the form of:
Ax + By + C = D
where:
Solving a linear equation involves finding the values of the variables that make the equation true. There are two main methods for solving linear equations:
Method 1: Elimination
Add or subtract the equations together.
Combine like terms on both sides.
Solve for one variable in terms of the other two.
Substitute the expression into the other equation.
Solve for the remaining variable.
Back-substitute the values of both variables into the original equations to check if they satisfy the equations.
Method 2: Substitution
Solve one equation for one variable in terms of the other two variables.
Substitute this expression into the other equation.
Solve for the remaining variable.
Back-substitute the values of both variables into the original equations to check if they satisfy the equations.
Tips for Solving Linear Equations:
Always isolate one variable on one side of the equation.
Pay attention to the coefficients of the variables in each equation.
Combine like terms on both sides of the equation using addition or subtraction.
Simplify the resulting expressions by combining like terms.
Check your answers by plugging them back into the original equations and verifying if they satisfy the conditions