To solve the equations such as this
there are common formulas
These formulas are easy to remember, if you introduce the concept of determinant of the second order as
Then the solution of the equations can be written as
ie each of the unknowns is equal to the fraction, the denominator of which is the determinant consisting of the coefficients of the unknowns and the numerator is obtained from this determinant by replacement of coefficients of the corresponding unknown to the absolute term.
There are three different solitions possible:
Coefficients at unknowns in equations are disproportionat
in this case the system of equations has a single solution, presented by formula
Coefficients at unknowns are proportional, but disproportionate to free terms
in this case the system of equations has no solutions, because we have here contradictory equations.
- All coefficients of equations are proportional
The system of equations has an infinite set of solutions, because we have actually one equation instead of two.