Question

Find the solution of x,y,z:
3x+y+2z=5
2x+3y+3z=3
x-2y-z=2

Answer 1

Infinitely many solutions

Explanation:

Step by Step Solution

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System of Linear Equations entered :

[1] 3x + y + 2z = 5

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

[3] x - 2y - z = 2

Solve by Substitution :

// Solve equation [3] for the variable x

[3] x = 2y + z + 2

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

[1] 3•(2y+z +2) + y + 2z = 5

[1] 7y + 5z = -1

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

[2] 2•(2y+z +2) + 3y + 3z = 3

[2] 7y + 5z = -1

// Solve equation [2] for the variable z

[2] 5z = -7y - 1

[2] z = -7y/5 - 1/5

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

[1] 7y + 5•(-7y/5-1/5) = -1

[1] 0 = 0 => Infinitely many