Use a matrix to find the solution to the systems of equations. Created by pumpkin1625. mathematics-us

The solutions of the system are: and ExplanationGiven system of equations......First we need to make the augmented matrix using the given equations....Now, we need to transform the augmented matrix to the reduced row echelon form using the row operations. Row operation 1 : Multiply the 1st row by . So, we will get...Row operation 2 : Add -6 times the 1st row to the 2nd row. So, we will get...Row operation 3 : Multiply the 2nd row by . So, we will get...Row operation 4 : Add -1 times the 2nd row to the 1st row. So, we will get....So, this is the reduced row echelon form.We can get the equations from the above reduced row echelon form as.....So, the solutions of the system are: and

Use a matrix to find the solution to the systems of equations

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pumpkin1625

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Use a matrix to find the solution to the systems of equations

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The solutions of the system are: $x=-6$ and $y=8$
Explanation
Given system of equations......
$-8x-8y=-16\\ \\ 6x-9y=-108$
First we need to make the augmented matrix using the given equations....
$\left[\begin{array}{cccc}-8&-8&|&-16\\6&-9&|&-108\end{array}\right]$
Now, we need to transform the augmented matrix to the reduced row echelon form using the row operations.
Row operation 1 : Multiply the 1st row by $-\frac{1}{8}$ . So, we will get...
$\left[\begin{array}{cccc}1&1&|&2\\6&-9&|&-108\end{array}\right]$
Row operation 2 : Add -6 times the 1st row to the 2nd row. So, we will get...
$\left[\begin{array}{cccc}1&1&|&2\\0&-15&|&-120\end{array}\right]$
Row operation 3 : Multiply the 2nd row by $-\frac{1}{15}$ . So, we will get...
$\left[\begin{array}{cccc}1&1&|&2\\0&1&|&8\end{array}\right]$
Row operation 4 : Add -1 times the 2nd row to the 1st row. So, we will get....
$\left[\begin{array}{cccc}1&0&|&-6\\0&1&|&8\end{array}\right]$
So, this is the reduced row echelon form.
We can get the equations from the above reduced row echelon form as.....
$1x+0y=-6\\ x=-6 \\ \\ and \\ \\ 0x+1y=8\\ y=8$
So, the solutions of the system are: $x=-6$ and $y=8$
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