Question

Please can anybody give me ans of Q 5 , how to solve this 3 equation and one unknown constant ?

Answer 1

x + y + z = 1 (this is equation 1)

3x+6y+z=1 (equation 2)

x + 2y + 3z =1(equation 3)

( There are many formulas to solve this but I will use eliminating method)

Multiplying 3 in eq-1 on both sides

3(x+y+z)=3(1)

3x + 3y + 3z = 3 (eq -4)

Subtracting eq 2 from eq 4

3x + 3y + 3z -(3x + 6y + z) =3-1

3x + 3y + 3z -3x -6y - z = 2

-3y + 2z =2 ( eq 5)

Now,

multiplying 3 on eq 3

3(x+2y + 3z) = 3(1)

3x + 6y + 9z = 3 ( eq 6)

Subtracting eq 2 from eq 6

3x + 6y + 9z -(3x +6y + z) =3-1

3x + 6y + 9z -3x-6y-z = 2

8z =2

z = 2/8

z=0.25

putting the value of z in Eq 5

-3y+ 2(0.25)=2

-3y +0.5 =2

-3y = 1.5

y = 1.5/-3

y =-0.5

Putting the value of y and z in eq 1

x + (-0.5)+0.25=1

x-0.5+0.25=1

x-0.25 =1

x=1.25

Therefore the value of x is1.25

the value of y is -0.5 and

the value of z is0.25