# simultaneous equations

Simultaneous equations are two or more equations that can be manipulated to give common solutions. In the simultaneous equations

*x* + 10*y* = 25, and

*x* + *y* = 7,

the problem is to find values of *x* and *y*, such that these
values are solutions of both the equations simultaneously. This can be done
by rearranging and combining the equations to obtain each of the unknown
variable sin turn. In this example, one equation can one equation can be
subtracted from the other to give 9*y* = 18, hence *y* = 2.
Substituting this value of *y* back into either of the equations
gives *x* = 5. In general, such systems of equations may have no
solutions, exactly one solution, or infinitely many solutions.