Question

Solve the following system. (Use (x, y) format)
x2 + y2 = 25
y2 - x2 = 7

Answer 1

There are several ways to solve this. Let's try substituting. We know that in a system of equations, all the equations use the same variables. That means that the x2 from one system is the same as the x2 from the other system--that's an important detail though. Is it supposed to be x2 as in x*2 or x2 as in x with the subscript of 2? Usually in algebra, we write the coefficient(the number on the variable) first.

Anyway, solve for y in terms of x in one of the equations and then substitute it back into the other equation. I will help you with this if you have additional trouble.

Answer 2

I understand. Thank you!

Answer 3

One of the most common mistakes when solving these types of problems is forgetting to distribute. For example:

x+y=25
-x+y=7

x=25-y

this is the key step. You should always substitute with parentheses, to make it clear to your teacher what you're doing, and to make it easier to avoid mistakes.
-(25-y)=7

-25+y=7

y=7+25=32