Question

Solve the following system of linear equations in three variables.

4(x + y) = 3(2z - y)
5(x - 2y) = 3(2y - 3z)
6(x - 2) + 7 (y - 3) + 8(z - 4) = 67

• A. x = 0.5, y = 10, z = 3
• B. x = 0.1, y = 8, z = 9.4
• C. x = 0.1, y = 8, z = 9.4
• D. x = 9.4, y = 0.1, z = 8

Answer 1

The correct option is B x = 0.1, y = 8, z = 9.4

4(x + y) = 3 (2z - y)
4x + 4y = 6z - 3y
4x + 7y - 6z = 0

5(x - 2y) = 3 (2y - 3z)
5x - 10y = 6y - 9z
5x - 16y + 9z = 0

6(x - 2) + 7(y - 3) + 8(z - 4) = 67
6x + 7y + 8z - 12 - 21 - 32 = 67
6x + 7y + 8z = 132

4x + 7y - 6z = 0 .....(1)
5x - 16y + 9z = 0 .....(2)
6x + 7y + 8z = 132 .....(3)


Now, substituting the value of 7 in eqn(4)
-7y + 34z = 264
-7y + 34(9.42) = 264.
-7y = - 55.6
$y=7.9\approx 8$
y = 8
Now, substituting the value of z and y in eqn(1)
4x + 7y - 6z = 0
$4x+7\times 8-6\times 9.4=0$
$4x-0.4=0$
x = 0.1