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

 

    x + 10y = 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 9y = 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.