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

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