Question

Solve

a.      x + y + z = 2, x – y + z = 3, x + y + 2z = 0

b.      5x + y – 2z = 2, x + 2y + 3z = 2, 2x – y = 3

Answer 1

a.

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

x-y+z = 3 .......(2)

x+y+2z = 0 .....(3)

add equation 1st and 2nd and 2nd and 3rd you will get

  2x+2z = 5 ....(4)

2x+3z = 3 ....(5)

subtracting equation 4 from 5 you will get

z = -2

now put the value of z in equation 4 you will get

x = 9/2

now put value of x and z into equation 1 so you will get

y = -1/2

so,

( 9/2 , -1/2 , -2) answer.

b.

5x+y-2z = 2 .....(1)

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

2x-y = 3 ......(3)

multiply equation 1 by 3 and equation 2 by 2 and then add equation 1 and 2 you will get

17x+7y = 10 .....(4)

by equation (3) and (4)

17x+7(2x-3) = 10

31x = 31

x = 1

now from equation 3

you will get

y = -1

now, from equation 1

z = 1

so

(1,-1,1) answer.