How do you solve the following system: #3x + 2y = 1, 2x + 3y = 12#?
The solution set is:
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:
I'm going to show you two methods to do this, namely Substitution and Elimination.
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
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