Question

8x-6y+2z=0,-6x+7y-4z=0 and 2x-4y+3z=0​

Answer 1

Step-by-step explanation:

[1] 8x - 6y + 2z = 0

[2] -6x + 7y - 4z = 0

[3] 2x - 4y + 3z = 0

// Solve equation [3] for the variable z

[3] 3z = -2x + 4y

[3] z = -2x/3 + 4y/3

// Plug this in for variable z in equation [1]

[1] 8x - 6y + 2•(-2x/3+4y/3) = 0

[1] 20x/3 - 10y/3 = 0

[1] 20x - 10y = 0

Plug this in for variable z in equation [2]

[2] -6x + 7y - 4•(-2x/3+4y/3) = 0

[2] -10x/3 + 5y/3 = 0

[2] -10x + 5y = 0

// Solve equation [2] for the variable y

[2] 5y = 10x

[2] y = 2x

Plug this in for variable y in equation [1]

[1] 20x - 10•(2x) = 0

[1] 0 = 0 => Infinitely many solutions

Answer 2

Answer:

8x-6y+2z=0,

-6x+7y-4z=0 and

2x-4y+3z=0

Input:

{8 x - 6 y + 2 z = 0, -6 x + 7 y - 4 z = 0, 2 x - 4 y + 3 z = 0}

Result:

{8 x - 6 y + 2 z = 0, -6 x + 7 y - 4 z = 0, 2 x - 4 y + 3 z = 0}

Alternate forms:

{4 x + z = 3 y, 6 x + 4 z = 7 y, 2 x + 3 z = 4 y}

{z = 3 y - 4 x, z = (7 y)\/4 - (3 x)\/2, z = (4 y)\/3 - (2 x)\/3}

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

Real solution:

y = 2 x, z = 2 x

Solution:

y = 2 x, z = 2 x