# Thread: How should I deal with this system of equations?

1. ## How should I deal with this system of equations?

$\displaystyle 0 = \frac{2}{3} + 2C + D$
$\displaystyle 0 = 2 +6B +6C + 4D + 4E$
$\displaystyle 6 = 10 + 12B - 6C +10D -5E$
$\displaystyle 0 = \frac{1}{3} + B + D$

I dont know where to start, since the first and last equations dont have any similar terms, what strategy is there for this?

2. ## Re: How should I deal with this system of equations?

Hello, Nervous!

Where did this problem come from?
The equations are clumsily written.

$\displaystyle \begin{array}{c}\tfrac{2}{3} + 2C + D \:=\:0 \\ 2 +6B +6C + 4D + 4E\:=\:0 \\ 10 + 12B - 6C +10D -5E \:=\:6 \\ \tfrac{1}{3} + B + D\:=\:0\end{array}$

First, I would eliminate the fractions, simplify, and write the equations in standard form.

. . $\displaystyle \begin{array}{cccccccccc} && 6C &+& 3D &&& = & -2 \\ 3B &+& 3C &+& 2D &+& 2E &=& -1 \\ 12B &-& 6C &+& 10D &_+& 5E &=& -4 \\ 3B &&& +& 3D &&& = & -1 \end{array}$

Then I would use my favorite method for solving a system of equations:
. . elimination, substitution, augmented matrix, Cramer's Rule, etc .

3. ## Re: How should I deal with this system of equations?

The algorithm is simple.
Step 1: Write the equations with variables on one side and constants on the other side.
Step 2: eliminate one by one the variables from the equations till you get two equations in two variables
Step 3: Find the values of two variables.
Step 4: Use these values to find the values of the other values.
Step : 5 You may verify the values by plugging in the values in the equations.

There is another method too that is by using matrices.
Go through the solution given on the attached sheet

4. ## Re: How should I deal with this system of equations?

Originally Posted by Soroban
Hello, Nervous!

Where did this problem come from?
It was a part of a larger, partial fraction integration, problem...

The 2/3 and other numbers in the front where the values of the A term.