Solution :
{x,y,z} = {4,-1,-3}
System of Linear Equations entered :
[1] 3x + 2y + z = 7
[2] 5x + 5y + 4z = 3
[3] 3x + 2y + 3z = 1
Solve by Substitution :
// Solve equation [1] for the variable z
[1] z = -3x - 2y + 7
// Plug this in for variable z in equation [2]
[2] 5x + 5y + 4•(-3x-2y+7) = 3
[2] -7x - 3y = -25
// Plug this in for variable z in equation [3]
[3] 3x + 2y + 3•(-3x-2y+7) = 1
[3] -6x - 4y = -20
// Solve equation [3] for the variable y
[3] 4y = -6x + 20
[3] y = -3x/2 + 5
// Plug this in for variable y in equation [2]
[2] -7x - 3•(-3x/2+5) = -25
[2] -5x/2 = -10
[2] -5x = -20
// Solve equation [2] for the variable x
[2] 5x = 20
[2] x = 4
// By now we know this much :
x = 4
y = -3x/2+5
z = -3x-2y+7
// Use the x value to solve for y
y = -(3/2)(4)+5 = -1
// Use the x and y values to solve for z
z = -3(4)-2(-1)+7 = -3
Solution :
{x,y,z} = {4,-1,-3}
Hope this has been explanatory enough
