Question

Given that x + 2y + 3z =1, 3x + 2y + z = 4, x + 3y + 2z = 0. What is x,y and z?

Answer 1

Answer:

Using a 3 x 4 matrix, and row operations, I get x = 9/2, y = -1, and z = -1/2.

Answer 2

The value of x= 7/4 , y= -3/4 , z= 1/4

Given,

x + 2y + 3z =1, 3x + 2y + z = 4, x + 3y + 2z = 0

To find,

Values of x,y and z

Solution,

Consider the given expressions as;

x + 2y + 3z =1 --- equation (1)

3x + 2y + z = 4 --- equation (2)

x + 3y + 2z = 0 --- equation (3)

To solve the values of x, y, and z, let us use the elimination method.

Elimination method:

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Subtract equation (3) from equation (1),

x + 2y + 3z =1

(-)

x + 3y + 2z = 0

here the x terms get canceled, and we get.,

z = 1+y --- equation (4)

In order to get a similar equation, multiply equation (1) by 3 and subtract with equation (2).

3x + 2y + z = 4

(-)

3x + 6y +9z = 3

here the x terms get canceled, and we get.,

-4y -8z = 1 --- equation (5)

substitute equation (4) with equation (5),

-4y - 8(1+y) = 1

-4y - 8 - 8y = 1

-12y = 9

y = -9/12

y = -3/4

Substitute the value of y in equation (4),

z = 1+ (-3/4)

z = 1/4

Hence, we got the values of y and z,

substitute them in equation (1) to get the value of x.

x + 2(-3/4) + 3(1/4) = 1

x - 6/4 + 3/4 = 1

x = 7/4

Therefore, the values of x = 7/4, y= -3/4, z= 1/4

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