# Construct the augmented matrix that corresponds to the following system of equations.5+(8x)/5=y2z−3(x−3y)=02x−y=3(x−4z)

Construct the augmented matrix that corresponds to the following system of equations.
$5+\frac{8x}{5}=y$
$2z-3\left(x-3y\right)=0$
$2x-y=3\left(x-4z\right)$

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Step 1:To determine:
Given:
System of equations:
$5+\frac{8x}{5}=y$
$2z-3\left(x-3y\right)=0$
$2x-y=3\left(x-4z\right)$
To determine:
The augmented matrix for the given system of equations.
Step 2:Calculation
Consider the equation $5+\frac{8x}{5}=y$
$⇒\frac{25+8x}{5}=y$
$⇒25+8x=5y$
$⇒8x-5y+0z=-25$...(1)
Consider the equation $2z-3\left(x-3y\right)=0$
$⇒2z-3x+9y=0$
$⇒-3x+9y+2z=0$...(2)
Consider the equation $2x-y=3\left(x-4z\right)$
$⇒2x-y=3x-12z$
$⇒2x-3x-y+12z=0$
$⇒-x-y+12z=0$...(3)
From equation 1,2,3, the augmented matrix is given by:
$\left[\begin{array}{cccc}9& -5& 0& -25\\ -3& 9& 2& 0\\ -1& -1& 12& 0\end{array}\right]$