Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution".
10x - 10y = 1
x = y - 3
10x - 10y = 1
x = y - 3
The second equation is solved for x, So substitute (y - 3) for x in the first equation 10x - 10y = 1
10(y - 3) - 10y = 1
10y - 30 - 10y = 1 -30 = 1
The y's all canceled out and left a false numerical equation, -30 in not equal to 1, so there is no solution. The system is called an inconsistent system of equation.