You just solve for x in both equations. You'll then have two equations that equal x, so then you make them equal each other. That'll tell you what number y is, so then you plug that number into either of the original equations to find what number x is: (1/3)x - (1/6)y = 1/2 Get rid of denominators by multiplying by a common denominator. Let's use 6: (6)(1/3)x - 6(1/6)y = 6(1/2) 2x - y = 3 Isolate x: 2x = 3 + y x = (3 + y)/2 Okay, now solve for x in the other equation: (x/5) - (3y/10) = 1/2 Multiply by a common denominator, 10 here, to get rid of the fractions: 10x/5 - 10(3y/10) = (10)(1/2) 2x - 3y = 5 Isolate x: 2x = 5 - 3y x = (5 - 3y)/2 Okay, now let's make both our x solutions equal each other to find what y really is: (5 - 3y)/2 = (3 + y)/2 (5 - 3y) = (3 + y) Let's move the constants to one side and the y's to the other side: 5 - 3 = 3y + y 2 = 4y 1/2 = y Okay, now we have y, let's find out what x is by plugging it into an earlier x solution: x = (3 + y)/2 x = (3 + 1/2)/2 x = (3.5)/2 = 1.75 So x = 1.75 and y = 0.5. Since we used fractions in our original equation, let's convert our decimals to fractions. x = 1 3/4 = 7/4 and y = 1/2 Let's check our work by plugging these numbers into an original equation: (1/3)x - (1/6)y = 1/2 (1/3)(7/4) - (1/6)(1/2) = 1/2 (7/12) - (1/12) = (6/12) = (1/2) It checks out. Good times.