Question

Consider the following system of equations.

a+b-4c=1
a+4b+c=12
a-3b-2c=-5
Show that (3,2,1) is a solution to the system

Answer 1

Explanation:

a+b-4c-a-4b-c=1-12, -3b-5c=-11

a+4b+c-a+3b+2c=12+5, 7b+3c=17

3(-3b-5c)+5(7b+3c)=3(-11)+5(17)

-9b-15c+35b+15c=-33+85

26b=52

b=2, making 7b+3c=17 become

14+3c=17

3c=3

c=1, making a+b-4c=1 become

a+2-4(1)=1

a-2=1

a=3

(a,b,c)=(3,2,1)