Quandaries and Queries
how do i know where to began the substitution method? how do i solve
y = x + 1
2x - y = 1
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
is equivalent to
Now solve this equation for x.
First remove the parentheses to get
Finally add 1 to each side of the equation
But your first equation told you that y is x + 1 so
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
If this were the case then, if you add x to each side you get
Then you can proceed as above. You could however have added -y to each side to get
Now multiply both sides by -1 to get
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.