Question

Solve the system of linear equations using the Gauss-Jordan elimination method. 5x + 3y = 16 −2x + y = −13 (x, y) =

Answer 1

This is it:

Explanation:

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Answer 2

The solution for this system is
`x = 5, y = 3`.

Explanation:

The Gauss-Jordan elimination method is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

We have the following system:

`5x + 3y = 16`

`-2x + y = -13`

This system has the following augmented matrix.

`\left[\begin{array}{ccc}5&3&16\\-2&1&-13\end{array}\right]`

The first step is dividing the first line by 5. So:

`L_(1) = (L_(1))/(5)`

We now have

`\left[\begin{array}{ccc}1&(3)/(5)&(16)/(5)\\-2&1&-13\end{array}\right]`

Now i want to reduce the first row, so I do:

`L_(2) = L_(2) + 2L_(1)`

So we have

`\left[\begin{array}{ccc}1&(3)/(5)&(16)/(5)\\0&(11)/(5)&-(33)/(5)\end{array}\right][\tex].</p><p>Now, the first step to reduce the second row is:</p><p>[tex]L_(2) = (5L_(2))/(11)`

So we have:

`\left[\begin{array}{ccc}1&(3)/(5)&(16)/(5)\\0&1&-3\end{array}\right]`.

Now, to reduce the second row, we do:

`L_(1) = L_(1) - (3L_(2))/(5)`

And the augmented matrix is:

`\left[\begin{array}{ccc}1&0&5\\0&1&-3\end{array}\right]`

The solution for this system is
`x = 5, y = 3`.