A system of equations consists of two or more linear equations with the same set of variables. Solutions to the system are the variable values that satisfy all the equations simultaneously.
5 Must Know Facts For Your Next Test
A system can be solved using various methods, including substitution, elimination, Gaussian elimination, and matrix inverses.
In Gaussian elimination, you convert the system's augmented matrix to row-echelon form to find solutions.
A consistent system has at least one solution; an inconsistent system has no solutions; a dependent system has infinitely many solutions.
Using matrix inverses to solve a system requires that the coefficient matrix be square (same number of rows and columns) and invertible (non-zero determinant).
Graphically, the solutions of a system correspond to the points where the equations' graphs intersect.