# How do you solve the following system: #3x + 2y = 1, 2x + 3y = 12#?

##### 2 Answers

The solution set is:

#### Explanation:

To make it easier, we take first the second equation and isolate x:

Then, we change x in the first equation for its new "value" and solve it:

We now have

So, the solution set is:

#### Explanation:

I'm going to show you two methods to do this, namely **Substitution** and **Elimination.**

**1. Substitution**

As the name suggests, we'll *substitute* one of the variables in terms of another.

We'll have to write

From the first equation we have:

Now that we have a value for

We can now substitute this value in any of the two equations in the beginning to get

**2. Elimination**

In this method, we'll first **eliminate** either the

I'm going to eliminate

In the first equation, the coefficient of

So let's make the coefficients of

Now, to eliminate the terms with

Now, like we did in the first step we can substitute this value of