Question

Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`

Answer 1

`[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`

∴ x + y = 2  .....(i)
   x - y = -1 ..........(ii)
y + z + w = 9 .....(iii)
2w - z = 5 ......(iv)

Adding equation (i) and (ii)

∴ `x + y = 2   

    x - y = -1
         2x = 1 ⇒ x = `1/2`

From equation (i)

`1/2 + y = 2 ⇒ y = 3/2`

Putting `y = 3/2` in equation (iii) we get

`3/2 + z + w = 9`

∴ `z + w = 9 - 3/2 = 15/2`

∴ `z + w = 15/2`  ....(v)

Adding equation (iv) and (v) we get

-z + 2w = 5
 z + w = `15/2`
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   `"3w" = 25/2 ⇒ "w" = 25/6`

From equation (v)

`z + 25/6 = 15/2 ⇒ 10/3`