How to solve linear simultaneous equations

 How to solve linear simultaneous equations

To solve a system of linear simultaneous equations, you can use various methods such as substitution, elimination, or matrix methods. I'll explain the steps for each method:

1. Substitution Method:
• Solve one equation for one variable in terms of the other variable.
• Substitute the expression obtained in step 1 into the other equation.
• Solve the resulting equation for the remaining variable.
• Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
• Check the solution by substituting the values obtained into both original equations.
2. Elimination Method:
• Multiply one or both equations by suitable constants so that the coefficients of one variable in both equations are the same or additive inverses of each other.
• Add or subtract the equations to eliminate one of the variables.
• Solve the resulting equation for the remaining variable.
• Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
• Check the solution by substituting the values obtained into both original equations.
3. Matrix Method (using augmented matrix):
• Write the system of equations in matrix form, where the coefficients of the variables form the matrix and the constants form the augmented column.
• Perform row operations to transform the matrix into row-echelon form or reduced row-echelon form.
• Read off the solutions from the transformed matrix.

It's worth noting that each method has its advantages and may be more suitable for certain types of problems. You can choose the method that you find most comfortable or appropriate for the given set of equations.