How do you solve the following system?: 11x+y-5z=1, 7x+13y+z=1, 8x-y-z=1111x+y5z=1,7x+13y+z=1,8xyz=11

1 Answer
Dec 29, 2015

11x+y-5z=111x+y5z=1..........(i)
7x+13y+z=1............(ii)
8x-y-z=11.............(iii)

Adding (ii) and (iii) we get
15x+12y=12
implies 5x+4y=4..........(iv)

Multiply (ii) by 5 and add in (i)

implies 35x+65y+5z=5
and 11x+y-5z=1

By addition we have

46x+66y=6

implies 23x+33y=3...............(v)

Multiply (iv) by 33 and (v) by 4 and subtract (v) from (iv)

implies 165x+132y=132
and 92x+132y=12

By subtraction we have
73x=120
implies x=120/73

Put x=120/73 in (iv)

implies 5(120/73)+4y=4

implies 600+292y=292

implies 292y=-308

implies y=-308/292=-77/73

implies y=-77/73

Put x=120/73 and y=-77/73 in (iii)

implies 8(120/73)-(-77/73)-z=11

implies z=8*120/73+77/73-11

implies z=960/73+77/73-11=(960+77-803)/73=234/73

implies z=234/73