Question

x+2y-z=6; -3-2y +5x=-12; x-2x=3​

Answer 1

Answer:

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x-2y+z=-6;-x+6y+4z=3;x+5z=-12

x-2y+z=-6;-x+6y+4z=3;x+5z=-12

Solution :

{x,y,z} = {3,3,-3}

System of Linear Equations entered :

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

[2] -x + 6y + 4z = 3

[3] x + 5z = -12

Solve by Substitution :

// Solve equation [3] for the variable x

[3] x = -5z - 12

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

[1] (-5z-12) - 2y + z = -6

[1] - 2y - 4z = 6

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

[2] -(-5z-12) + 6y + 4z = 3

[2] 6y + 9z = -9

// Solve equation [2] for the variable z

[2] 9z = -6y - 9

[2] z = -2y/3 - 1

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

[1] - 2y - 4•(-2y/3-1) = 6

[1] 2y/3 = 2

[1] 2y = 6

// Solve equation [1] for the variable y

[1] 2y = 6

[1] y = 3

// By now we know this much :

x = -5z-12

y = 3

z = -2y/3-1

// Use the y value to solve for z

z = -(2/3)(3)-1 = -3

// Use the z value to solve for x

x = -5(-3)-12 = 3

Solution :

{x,y,z} = {3,3,-3}