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Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5
Solution:
Given is a system of linear equations of 3 variables.
2x + 3y - z = 1 --- (1)
⇒ 3x + y + 2z = 12 --- (2)
⇒ x + 2y - 3 = - 5
⇒ x + 2y = - 2 --- (3)
Let us use the substitution method for solving the system of linear equations simultaneously.
By solving equation [1] for the variable z, we get
⇒ z = 2x + 3y - 1..............(4)
Substitute the value of z = 3x + 6y - 1 in equation [2]
⇒ 3x + y + 2× (2x + 3y - 1 ) = 12
⇒ x + y = 2 .............. (5)
By subtracting equation (5) from (3), we get
y = - 4
Substitute the value of y = - 4 in equation [5]
⇒ x + (- 4) = 2
⇒ x = 6
Substitute the values of x and y in equation (1), we get
⇒ 2 (6) + 3 (- 4) - z = 1
⇒ 12 - 12 - z = 1
⇒ 0 - z = 1
⇒ z = -1
Solve the following system of equation; 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5
Summary:
By solving the system of linear equations 2x + 3y - z = 1, 3x + y + 2Z = 12, x + 2y - 3 = - 5 ; we get (x, y, z) = (6, - 4, -1).
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