Question

Solve the equations x + 4y + 3z – 2 = 0, 2x – 6y + 6z + 3 = 0,
5x + 3z = -5 + 2y by the method of determinants.​

Answer 1

Answer:

x= -1

y=1/2

z=1/3

explained in picture

Answer 2

Given :

x + 4y + 3z = 2,  2x – 6y + 6z = –3,  5x – 2y + 3z = –5  

To Find : Solve  for x , y and z with the help of determinant method.

Solution:

x + 4y + 3z = 2,

2x – 6y + 6z = - 3

5x – 2y + 3z = –5  

$x=\frac{ \left|\begin{array}{ccc}2&4&3\\-3&-6&6\\-5&-2&3\end{array}\right| }{ \left|\begin{array}{ccc}1&4&3\\2&-6&6\\5&-2&3\end{array}\right| }$

=> x = -168/168  = - 1

$y=\frac{ \left|\begin{array}{ccc}1&2&3\\2&-3&6\\5&-5&3\end{array}\right| }{ \left|\begin{array}{ccc}1&4&3\\2&-6&6\\5&-2&3\end{array}\right| }$

y = 84/168  = 1/2

$z=\frac{ \left|\begin{array}{ccc}1&4&2\\2&-6&-3\\5&-2&-5\end{array}\right| }{ \left|\begin{array}{ccc}1&4&3\\2&-6&6\\5&-2&3\end{array}\right| }$

z = 56/168  = 1/3

x = - 1  , y = 1/2  , z  = 1/3

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