Suppose I have an equation x+2y=3 and label it (2). And I have a previous equation x+y=2 labeled (1). Now I want to put the two equations together and solve them, what should I write?
I truly believe that the best phrase to say what you described in your question is solving equations, or solving a set of equations, or solving a system of equations.
It is worth mentioning that there are many approaches and methods to solve a system of equations. We can solve it algebraically. We can solve it numerically. We can solve it by using elementary algebra. We can also treat the whole set of equations as a matrix and solve it with a method called row reduction (also known as Gaussian elimination).
However, I usually prefer the simplest choice when I have many. And I would like to quote from this page in Wikipedia,
The simplest kind of linear system involves two equations and two variables:
One method for solving such a system is as follows. First, solve the top equation for x in terms of y:
Now substitute this expression for x into the bottom equation:
This results in a single equation involving only the variable y. Solving gives y = 1, and substituting this back into the equation for x yields x = 3/2. This method generalizes to systems with additional variables (see "elimination of variables" below, or the article on elementary algebra.)
The example above should illustrate how to describe mathematical operations we needed in order to solve a set of equations well enough.
I wanted to give you a few more options that are less formal than the other answers. In a mathematical proof where I can assume that the reader already knows about systems of linear equations and Gaussian elimination, I'll sometimes use the following constructions:
Using equations (1) and (2), solve for x and y:
Combine equations (1) and (2):
x = 1
y = 1
I don't know in what way you mean by "put the two together". All I can think of is that:
You want to solve the y and x with addition method. Write them like:
x+2y=3 (2) -
If we add the two equations (or in this case, subtract Eq. 1 from Eq.2), we will get -y = -1, therefore y=1. Next, we substitute 1 in for y into any one of the equations. If we choose to substitute in the first equation, we will get x = 1.
P.S. This is also called elimination method for linear equation. There are some other methods too, like Gaussian Elimination, Substitution, Graphing, Matrices, etc. These methos are usually used for linear equations (linear inequalities). As for the non-linear ones, you have to solve them in other ways. For example, use factoring for quadratic equations,
P.P.S*: Based on Frank's comment, this would form a system of linear equations which can be solved some methods, one of which is addition/elimination.