# How do you solve using gaussian elimination or gauss-jordan elimination, x+2y=7 , 3x-2y=-3?

Jun 21, 2017

$x = 1$ and $y = 3$

#### Explanation:

Rewrite this system in matrix form
|1 2] $\left[x\right]$ $= \left[7\right]$
|3 -2] $\left[y\right]$ $\left[- 3\right]$

Now we want to put this matrix in triangular form. This amounts to eliminating y for instance.

[1 2] [x] = [7]
[4 0] [y] [4]

In this form, you see that triangular means one equation will have all zero matrix element except one. In our case the bottom equation reads

$4 x = 4$
The equation right above will have two non-zero matrix elements. Using the solution from the bottom equation, you can plug this solution into the equation above to get
$x + 2 y = 7$
$1 + 2 y = 7$
or $2 y = 6$
That is $y = 3$

Check
$x + 2 y = 1 + 2 \cdot 3 = 7$
$3 x - 2 y = 3 - 6 = - 3$

That method only becomes efficient when you have more than two variables.