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Question
Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`
Solution
`[("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`
__________________
`"3w" = 25/2 ⇒ "w" = 25/6`
From equation (v)
`z + 25/6 = 15/2 ⇒ 10/3`
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