Question

Use Cramer's rule to solve the system. 2x + 4y - z = 32 x - 2y + 2z = -5 5x + y + z = 20

Answer 1

A) 2x + 4y - z = 32

B) x - 2y + 2z = -5

C) 5x + y + z = 20

We will assign letters to each of the 12 numbers in the 3 equations.
a = 2
b = 4
c = -1
d = 1
e = -2
f = 2
g = 5
h = 1
i = 1
j = 32
k = -5
l = 20
We first must calculate the denominator determinant

dn = (a•e•i) + (b•f•g) + (c•d•h) - (g•e•c) - (h•f•a) - (i•d•b)
dn = (2*-2*1) + (4*2*5) + (-1*1*1) - (5*-2*-1) -(1*2*2) -(1*1*4)

dn = -4  + 40 + -1 - 10  - 4  -4
dn = 17

Now, we'll solve for x with this equation:
x= (j•e•i) + (b•f•l) + (c•k•h) -(l•e•c) -(h•f•j) -(i•k•b) ÷ dn
x = [(32*-2*1) + (4*2*20) + (-1*-5*1) -(20*-2*-1) -(1*2*32) -(1*-5*4)] / 17
x = (-64 +160 +5 -40 -64 +20) / 17
x =  17 / 17
x = 1

Solving for "y"
y = [(a• k• i) + (j• f• g) + (c• d• l) - (g• k• c) - (l• f• a) - (i• d• j)] ÷ dn
y = [(2*-5*1) + (32*2*5) + (-1*1*20) -(5*-5*-1) -(20*2*2) -(1*1*32)] / 17
y = [-10 + 320 -20 -25 -80 -32] / 17
y = 153 / 17
y = 9

Solving for "z"
z = [(a• e• l) + (b• k• g) + (j• d• h) - (g• e• j) - (h• k• a) - (l• d• b)] ÷ dn
z = [(2*-2*20) + (4*-5*5) + (32*1*1) -(5*-2*32) -(1*-5*2)-(20*1*4)] / 17
z = (-80 -100 +32 +320 +10 -80) / 17
z = 102 / 17
z = 6

Source:
http://www.1728.org/cramer.htm