Question

0.3
Solve the following system of linear eqnations.
x + y - 3z + 2w=0
2x - y + 2z - 3w = 0
3x - 2y + z- 4w=0
4x +y - 32+ w=0​

Answer 1

Answer:

1] x + y - 3z + 2w = 0

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

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

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

Solve by Substitution :

// Solve equation [4] for the variable w

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

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

[1] x + y - 3z + 2•(-4x-y +3z) = 0

[1] -7x - y + 3z = 0

// Plug this in for variable w in equation [2]

[2] 2x - y + 2z - 3•(-4x-y +3z) = 0

[2] 14x + 2y - 7z = 0

// Plug this in for variable w in equation [3]

[3] 3x - 2y + z - 4•(-4x-y +3z) = 0

[3] 19x + 2y - 11z = 0

// Solve equation [1] for the variable y

[1] y = -7x + 3z

// Plug this in for variable y in equation [2]

[2] 14x + 2•(-7x+3z) - 7z = 0

[2] - z = 0

// Plug this in for variable y in equation [3]

[3] 19x + 2•(-7x+3z) - 11z = 0

[3] 5x - 5z = 0

// Solve equation [2] for the variable z

[2] z = 0

// Plug this in for variable z in equation [3]

[3] 5x - 5•() = 0

[3] 5x = 0

// Solve equation [3] for the variable x

[3] 5x = 0

[3] x = 0

// By now we know this much :

x = 0

y = -7x+3z

z = 0

w = -4x-y+3z

// Use the x and z values to solve for y

y = -7(-0/32765)+3(0) = 0 // Use the x, y and z values to solve for w

w = -4(-0/32765)-(0)+3(0) = 0