Question

the sum of 3 numbers is 6. if we multiply third number by 3 and add it to the second number we get 11.by adding first and third number we get a number which is double the second number use this information and find a system of linear equation.find the 3 number using matrices

Answer 1

Let the numbers be a,b,c
By the problem,
a+b+c=6----------(1)
3c+b=11----------(2)
a+c=2b------------(3)
Substituting (3) in (1),
2b+b=6
3b=6
b=2-------(4)
From (3) b=(a+c)/2-------(5)
substituting (5) in (2),
3c+(a+c)/2=11
(6c+a+c)/2=11
(7c+a)/2=11
7c+a=22----------(6)
Substituting (4) in (3),
a+c=2(2)
a+c=4
a=4-c--------(7)
Substituting (7) in (6),
7c+4-c=22
6c+4=22
6c=18
c=3--------(8)
Substituting (8),(4) in (1),
a+2+3=6
a+5=6
a=6-5
a=1.
Therefore the three numbers are 1,2,3.

Answer 2

x+y+z=6
3z+y=11+
3z=11-y
z=$\frac{11-y}{3}$
z+x=2y
$\frac{11-y}{3}$+x=2y
[tex] \frac{(11-y)+x}{3}=2y \\ 6y+y-11=x \\ 7y-11=x \\ \\ we know z= \frac{11-y}{3} \\ put this in eqn 1 \\ \\ 7y-11+y+ \frac{11-y}{3} \\ = \frac{(8y-11)*3+11-Y}{3} \\ [/tex]
18+33-11=24Y-Y
23Y=40
Y=40/23