Question

The system of equations is given:

Answer 1

Answer:

x=-1/85; y=-283/85; z=2/17

Step-by-step explanation:

Using an algebraic method like elimination or substitution would take a lot of steps which could lead to mistake the calculations. In this case, I decided to use the Gaussian elimination. We can express the system in matrix form as follows:

$\left[\begin{array}{ccc}2&-4&6\\9&-3&1\\5&0&9\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}14\\10\\1\end{array}\right]$

To begin the calculations, we write the system in augmented matrix form and use the Gaussian elimination:

$\left[\begin{array}{ccccc}2&-4&6&|&14\\9&-3&1&|&10\\5&0&9&|&1\end{array}\right]$

By applying the Gaussian elimination, the final matrix is the following:

$\left[\begin{array}{ccccc}1&0&0&|&-1/85\\0&1&0&|&-283/85\\0&0&1&|&2/17\end{array}\right]$

In order to verify the results, it´s enough to substitute the calculated values in the original equations to see if the equalities are correct. Here you can see the verification for all of the equations:

$2(-1/85)-4(-283/85)+6(2/17)=14\\9(-1/85)-3(-283/85)+1(2/17)=10\\5(-1/85)+9(2/17)=1$