Solve each of the following systems of equations using matrix method.

4x + 3y + 2z = 60;


x + 2y + 3z = 45;


6x + 2y + 3z = 70.



To find: - x , y , z


Given set of lines are : -


4x + 3y + 2z = 60


x + 2y + 3z = 45


6x + 2y + 3z = 70


Converting the following equations in matrix form,


AX = B



4R2 – R1


2R3 – 3R1



Again converting into equations, we get


4x + 3y + 2z = 60


5y + 10z = 120


- 5y = - 40


Y = 8


5×8 + 10z = 120


10z = 120 - 40


10z = 80


Z = 8


4x + 3×8 + 2×8 = 60


4x = 60 – 24 - 16


4x = 20


X = 5


x = 5 , y = 8 , z = 8


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