Simutenous equation
A simultaneous equation, also known as a system of equations, is a set of two or more equations that share common variables. The goal is to find values for the variables that satisfy all of the given equations simultaneously.
To solve a system of simultaneous equations, you can use different methods. Here, I will explain three commonly used methods:
1. Substitution Method:
- Solve one equation for one variable in terms of the other variable.
- Substitute the expression obtained from step 1 into the other equation, replacing the variable.
- Solve the resulting equation for the remaining variable.
- Substitute the value found in step 3 back into either of the original equations to find the value of the first variable.
- Check the solution by substituting the values back into both equations.
2. Elimination Method:
- Multiply one or both equations by constants so that the coefficients of one variable in both equations are additive inverses.
- Add or subtract the modified equations together to eliminate one variable and solve the resulting equation for the remaining variable.
- Substitute the value found in step 2 back into either of the original equations to find the value of the first variable.
- Check the solution as explained above.
3. Matrix Method (Cramer’s Rule):
- Arrange the coefficients of the variables in matrix form, along with a column matrix of the constants.
- Find the determinants of the coefficient matrix and the matrices obtained by replacing one column with the constants.
- Divide the determinant of each replacement matrix by the determinant of the coefficient matrix to find the values of the variables.
- Check the solution as explained above.
Remember, it's important to check your solution by substituting the values back into both equations to ensure they satisfy all given equations.