System of two linear equations
System of two equations is generally given as
It has
- a unique solution, if lines are not parallel.
- no solution, if lines are parallel but not equal.
- infinite number of solutions, if line are exactly the same.
- Solve one variable from the first equations.
- Substitute the solution to the unknown in the second equation. Now, there is normal linear equation to be solved.
- Solve the linear equation.
- Substitute the solution to the first equations in order to find solution for the second variable.
- Check your solution by substituting bot solution to both original equations (not only to one equation).
Elimination method:
- Multiply or divide both the linear equations with a non-zero number to get a common opposite coefficient of any one of the variables in both equations.
- Add both the equations such that the same terms will get eliminated.
- Solve the linear equation.
- Substitute this value in any of the given equations to find the value of the other given variable.
- Check your solution by substituting bot solution to both original equations (not only to one equation).
Example 1.
Solve
Multiply equations so that multipliers of one variable are opposite numbers:
Add equations so, that only one variable is left:
After this, the second variable can be solved from any equation:
The solution is check by substituting to the original equations:
As solutions in the second equation gives the same value as given at the right side, solution seems to be fine.