Solving a Linear Equation in Two Variables A linear equation in two variables has the general form of: Ax + By = C where: A is the coefficient of...
A linear equation in two variables has the general form of:
Ax + By = C
where:
A is the coefficient of x
B is the coefficient of y
C is the constant term
Solving a linear equation means finding the values of x and y that make the equation true. This can be done by using different methods, such as isolating x or y on one side of the equation.
Steps to solve a linear equation:
A: This is the coefficient of x.
B: This is the coefficient of y.
Subtract Ax from both sides of the equation.
Subtract By from both sides of the equation.
Divide both sides of the equation by A (if A is not equal to 0).
Divide both sides of the equation by B (if B is not equal to 0).
Examples:
Example 1:
3x + 2y = 7
Isolate the variable:
Subtract 2y from both sides:
3x = 7 - 2y
Solve for x:
Divide both sides by 3:
x = (7 - 2y) / 3
Example 2:
x - 4y = 3
Isolate the variable:
Add 4y to both sides:
x = 3 + 4y
Solve for y:
Subtract x from both sides:
4y = 3 - x
Solve for x:
Divide both sides by 4:
x = (3 - 4y) / 4
Tips for solving linear equations:
Always check your solutions to ensure they make sense.
If the coefficient of either variable is 0, the equation will always be true.
You can use the same methods to solve linear equations in three or more variables