What are 3 ways to solve system of linear equations in two variables?
Addition, subtraction, substitution?
There are several methods to solve a system of linear equations in two variables. Here are three commonly used methods:
1. Graphing Method:
- Step 1: Graph both equations on the same coordinate plane.
- Step 2: Identify the point of intersection, if it exists. This point represents the solution to the system of equations.
- Step 3: If there is no point of intersection, then the system doesn't have a solution.
2. Substitution Method:
- Step 1: Solve one equation for one variable in terms of the other variable.
- Step 2: Substitute the expression obtained in step 1 into the other equation.
- Step 3: Solve the resulting equation for the remaining variable.
- Step 4: Substitute the value found in step 3 back into either of the original equations and solve for the other variable.
- Step 5: The solution is the values of both variables.
3. Elimination Method (also known as the Addition/Subtraction Method):
- Step 1: Multiply one or both equations by suitable constant(s) so that the coefficients of one variable in both equations will be additive inverses (positive and negative).
- Step 2: Add or subtract the two equations to eliminate one of the variables.
- Step 3: Solve the resulting equation for the remaining variable.
- Step 4: Substitute the value found in step 3 back into either of the original equations and solve for the other variable.
- Step 5: The solution is the values of both variables.
These three methods can be used to solve a system of linear equations in two variables. Depending on the specific situation and the equations involved, one method may be more efficient or easier to use than the others.