 Quandaries and Queries Addie student middle(6-9)     how do i know where to began the substitution method? how do i solve   y = x + 1 2x - y = 1 Hi Addie, The first equation tells you that y and x + 1 are the same quantity. Hence, in the second equation, wherever you see y you can replace it by x + 1. Thus 2x - y = 1 is equivalent to 2x - (x + 1) = 1 Now solve this equation for x. First remove the parentheses to get 2x - x - 1 = 1 or x - 1 = 1 Finally add 1 to each side of the equation x - 1 + 1 = 1 + 1 x = 2 But your first equation told you that y is x + 1 so y = x + 1 = 2 + 1 = 3 You should now check that x = 2 and y = 3 satisfy the equations you started with. Sometimes you need to perform an extra step to apply the substitution method. Suppose that the first equation had been y - x = 1 If this were the case then, if you add x to each side you get y - x + x = x + 1 or y = x + 1 Then you can proceed as above. You could however have added -y to each side to get y - x - y = 1 - y which is -x = 1 - y Now multiply both sides by -1 to get x = -1 + y If you now replace x in the second equation by -1 + y you will get an equation in y which you can solve. Try it! you should get the same answer I got, y = 3. Penny Go to Math Central