Answer:
Step-by-step explanation:
x-3y-z=-9;-2x+y+2z=3;2x+y+3z=8
Solution :
{x,y,z} = {1,3,1}
System of Linear Equations entered :
[1] x - 3y - z = -9
[2] -2x + y + 2z = 3
[3] 2x + y + 3z = 8
Solve by Substitution :
// Solve equation [3] for the variable y
[3] y = -2x - 3z + 8
// Plug this in for variable y in equation [1]
[1] x - 3•(-2x-3z+8) - z = -9
[1] 7x + 8z = 15
// Plug this in for variable y in equation [2]
[2] -2x + (-2x-3z+8) + 2z = 3
[2] -4x - z = -5
// Solve equation [2] for the variable z
[2] z = -4x + 5
// Plug this in for variable z in equation [1]
[1] 7x + 8•(-4x+5) = 15
[1] -25x = -25
// Solve equation [1] for the variable x
[1] 25x = 25
[1] x = 1
// By now we know this much :
x = 1
y = -2x-3z+8
z = -4x+5
// Use the x value to solve for z
z = -4(1)+5 = 1
// Use the x and z values to solve for y
y = -2(1)-3(1)+8 = 3
Solution :
{x,y,z} = {1,3,1}
