Answer:
a) x = -37 , y = -8, z = 5.
b) w = 13z-10, x = 13z-5, y= 2-z, z = free parameter.
c) v = 2z-7w-11, w = free parameter, x = -3z-4, y = 9-3z, z = free parameter
d) No solution
Step-by-step explanation:
a)
The following set of equations are:
z = 5
y+2z=2
x-3y+4z=7
Solving above equations:
y = -8, x = 7-4(5)+3(-8) = -37
b)
The following set of equations are:
y+z = 2
x+4y-9z=3
w+8y-5z=6
Solving above equations:
z = free parameter - No. of columns > No. of rows; hence, multiple solutions.
y = 2-z, x = 3+9z-4(2-z) = -5+13z, w = 6+5z-8(2-z) = 13z-10
c)
The following set of equations are:
y + 3z = 9
x + y + 6z = 5
v + 7w -2x -8z = -3
Solving above equations:
z & w = free parameter - No. of columns > No. of rows; hence, multiple solutions.
y = 9-3z, x = -3z-4, v = -11+2z-7w
d)
The following set of equations are:
0 = 1
y + 4z = 0
x-3y+7z = 1
Solving above equations:
No Solution as the first equation is inconsistent