Question

solve by matrix method x+y+2z=4 2x-y+3z =9 3x-y-z=2

Answer 1

Step-by-step explanation:

/ Solve equation [1] for the variable y

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

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

[2] 2x - (-x -2z+4) + 3z = 9

[2] 3x + 5z = 13

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

[3] 3x - (-x -2z+4) - z = 2

[3] 4x + z = 6

// Solve equation [3] for the variable z

[3] z = -4x + 6

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

[2] 3x + 5•(-4x+6) = 13

[2] -17x = -17

// Solve equation [2] for the variable x

[2] 17x = 17

[2] x = 1

// By now we know this much :

x = 1

y = -x-2z+4

z = -4x+6

// Use the x value to solve for z

z = -4(1)+6 = 2

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

y = -(1)-2(2)+4 = -1