Question

3x+2y+7z=0,4x-3y-2z=0,5x+9y+23z=0 solve the following system of homogeneous equations

Answer 1

Given:

3x + 2y + 7z = 0, 4x - 3y - 2z = 0, 5x + 9y + 23z = 0

To find:

Solve the following system of homogeneous equations

Solution:

From given, we have the system of homogeneous equations

3x + 2y + 7z = 0......(1)

4x - 3y - 2z = 0........(2)

5x + 9y + 23z = 0 .......(3)

(1) × 4 - (2) × 3 gives,

12x + 8y + 28z = 0

12x - 9y - 6z = 0

solving these equations, we get,

17y + 34z = 0

y = - 2z

equating the value of y in equation (1), we get,

3x + 2(-2z) + 7z = 0

3x - 4z + 7z = 0

3x + 3z = 0

x = -z

Therfore, the solutions of the given system of equations, we have,

x = -z and y = -2z