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:
- 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.
- 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.
- 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.
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