I will try to solve your system of equations. 3 x − 4 y = 2 ; 9 x − 12 y = 6 Step: Solve 3 x − 4 y = 2 for x: 3 x − 4 y + 4 y = 2 + 4 y (Add 4y to both sides) 3 x = 4 y + 2 3 x 3 = 4 y + 2 3 (Divide both sides by 3) x = 4 3 y + 2 3 Step: Substitute 4 3 y + 2 3 for x in 9 x − 12 y = 6 : 9 x − 12 y = 6 9 ( 4 3 y + 2 3 ) − 12 y = 6 6 = 6 (Simplify both sides of the equation) 6 + − 6 = 6 + − 6 (Add -6 to both sides) 0 = 0 Answer: Infinitely many solutions.