Question

2x+y-3z=-4 4x-2y+z=9 3x+5y-2z=5 solve by gauss elimination method​

Answer 1

Answer:

System of Linear Equations entered :

[1] 2x + y - 3z = -4

[2] 4x - 2y + z = 9

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

Solve by Substitution :

// Solve equation [2] for the variable z

[2] z = -4x + 2y + 9

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

[1] 2x + y - 3•(-4x+2y+9) = -4

[1] 14x - 5y = 23

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

[3] 3x + 5y - 2•(-4x+2y+9) = 5

[3] 11x + y = 23

// Solve equation [3] for the variable y

[3] y = -11x + 23

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

[1] 14x - 5•(-11x+23) = 23

[1] 69x = 138

// Solve equation [1] for the variable x

[1] 69x = 138

[1] x = 2

// By now we know this much :

x = 2

y = -11x+23

z = -4x+2y+9

// Use the x value to solve for y

y = -11(2)+23 = 1

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

z = -4(2)+2(1)+9 = 3

Solution :

{x,y,z} = {2,1,3}