Question

3x - 4y = 6z,-16, 4x-y-z = 5, x = 3y + 2(z+1)​

Answer 1

Step-by-step explanation:

3x-4y-6z=-16;4x-y-z=5;x-3y-2z=-2

Solution :

{x,y,z} = {2,-2,5}

System of Linear Equations entered :

[1] 3x - 4y - 6z = -16

[2] 4x - y - z = 5

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

Solve by Substitution :

// Solve equation [3] for the variable x

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

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

[1] 3•(3y+2z-2) - 4y - 6z = -16

[1] 5y = -10

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

[2] 4•(3y+2z-2) - y - z = 5

[2] 11y + 7z = 13

// Solve equation [1] for the variable y

[1] 5y = - 10

[1] y = - 2

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

[2] 11•(-2) + 7z = 13

[2] 7z = 35

// Solve equation [2] for the variable z

[2] 7z = 35

[2] z = 5

// By now we know this much :

x = 3y+2z-2

y = -2

z = 5

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

x = 3(-2)+2(5)-2 = 2

Solution :

{x,y,z} = {2,-2,5}

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