Question

4x+3y+2z=60; 2x+4y+6z=90; 6x+2y+3z=70, find x, y, z by reduction method

Answer 1

the correct solution of the question

Answer 2

Given : 4x+3y + 2z = 60, 2x+4y +6z =90 and 6x +2y+3z = 70

To Find :  Solve using matrix method

Solution:

4x+3y + 2z = 60

2x+4y +6z =90  

6x +2y+3z = 70

$\left[\begin{array}{ccc}4&3&2\\2&4&6\\6&2&3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}60\\90\\70\end{array}\right]$

AX = B

X = A⁻¹B

A⁻¹  =  Adj A / |A|

|A| = 4(12 - 12)  - 3(6-36) + 2 ( 4 - 24)

= 0  + 90 - 40

= 50

Adj A  =

$\left[\begin{array}{ccc}0&-5&10\\30&0&-20\\-20&10&10\end{array}\right]$

X = A⁻¹B

$X=\dfrac{1}{50} \left[\begin{array}{ccc}0&-5&10\\30&0&-20\\-20&10&10\end{array}\right]\left[\begin{array}{ccc}60\\90\\70\end{array}\right]$

$X=\dfrac{1}{50} \left[\begin{array}{ccc}250\\400\\400\end{array}\right]$

$X= \left[\begin{array}{ccc}5\\8\\8\end{array}\right]$

x = 5

y = 8

z = 8

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