Question

(ii) x+6y=5z. x+z=6y 5x+6y-4z=24

Answer 1

Given that

x+6y = 5z                    ..........................Eq.(1)

x+z = 6y                      ..........................Eq.(2)

5x+6y-4z = 24              ..........................Eq.(3)

From Eq.(1)

x = 5z-6y

Substituiting the value of x into Eq.(2)

(5z-6y)+z = 6y

=> 6z = 12y

=> z = 2y               .......................Eq.(4)

Substituting the value of x into Eq.(3)

5(5z-6y)+6y-4z = 24

=> 25z-30y+6y-4z = 24

=> 21z-24y = 24   ........................Eq.(5)

Multiplying Eq.(4) by 12

=> 24y = 12z        .........................Eq.(6)

Adding Eq.(5) and Eq.(6)

=> 21z = 24+12z

=> 9z = 24

=> z = 24/9

Substituiting the value of z into Eq.(4)

=> 24/9 = 2y

∴ y = 12/9

Substituiting the values of y and z into Eq.(1)

 x = 5(24/9) - 6(12/9)

=> x = 120/9-72/9

∴ x = 48/9 = 16/3

Thanks!!!