Question

x=y-2z, 2y=x+3z+1,z=2y-2x-3,solve by elimination method​

Answer 1

Step by Step Solution

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System of Linear Equations entered :

[1] x=y-2z

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

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

Equations Simplified or Rearranged :

[1] x - y + 2z = 0

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

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

Solve by Substitution :

// Solve equation [3] for the variable z

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

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

[1] x - y + 2•(-2x+2y-3) = 0

[1] -3x + 3y = 6

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

[2] -x + 2y - 3•(-2x+2y-3) = 1

[2] 5x - 4y = -8

// Solve equation [2] for the variable x

[2] 5x = 4y - 8

[2] x = 4y/5 - 8/5

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

[1] -3•(4y/5-8/5) + 3y = 6

[1] 3y/5 = 6/5

[1] 3y = 6

// Solve equation [1] for the variable y

[1] 3y = 6

[1] y = 2

// By now we know this much :

x = 4y/5-8/5

y = 2

z = -2x+2y-3

// Use the y value to solve for x

x = (4/5)(2)-8/5 = 0

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

z = -2(0)+2(2)-3 = 1