Question

:( Our professor has not shared the lecture notes yet (he doesn't let us write in class unless we're working out a problem, Dumb thing to do I know) and I have such a horrible memory with math especially with dealing with fractions. I can't remember how we did the similar problem today. Please explain step by step with this equation i'm going to provide. :) Thank you kind Stranger(s) for taking the time to answer it.
If x−y=2 and x=5/2, find y.

Answer 1

Answer:

y = 1/2

Step-by-step explanation:

Notice in this equation (x − y = 2) that there is "x".

Look at the other equation; it also has "x" (x = 5/2).

When the same variable is used, it has to be the same number.

Therefore x = x in both equations.

You can substitute, or replace one of the "x" with a value that another "x" is equal to      =>   x = 5/2

We can replace the "x" in x − y = 2 using 5/2.

Take the longer equation

x − y = 2

(5/2) − y = 2           Substitute the value of "x"

5/2 − y = 2             Remove the brackets, they are not needed

Now isolate "y" to solve. This means to move everything that is not "y" to the right side, keeping "y" on the left.

When you move a number, do its reverse operation to the whole equation.

5/2 − 5/2 − y = 2 − 5/2            Subtract 5/2 on both sides

−y = 2 − 5/2                       The 5/2's cancelled out on the left

Change "2" into fraction form because you need to subtract a fraction.

−y = $\frac{2}{1}-\frac{5}{2}$

−y = $\frac{2*2}{1*2}-\frac{5}{2}$           Use a common denominator

−y = $\frac{4}{2}-\frac{5}{2}$        Both denominators are the same

−y = $\frac{4-5}{2}$          Combine over the same denominator

−y = $\frac{-1}{2}$             Subtracted the numerators.

−y = $-\frac{1}{2}$             Rewrite the negative

−y/-1 = $-\frac{1}{2}/-1$             Divide both sides by -1

y = $\frac{1}{2}$                  Answer, solved for "y"