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Byju's Answer
Standard XII
Mathematics
Derivative of One Function w.r.t Another
x + y + z + w...
Question
x + y + z + w = 2
x − 2y + 2z + 2w = − 6
2x + y − 2z + 2w = − 5
3x − y + 3z − 3w = − 3
Open in App
Solution
D
=
1
1
1
1
1
-
2
2
2
2
1
-
2
2
3
-
1
3
-
3
1
-
2
2
2
1
-
2
2
-
1
3
-
3
-
1
1
2
2
2
-
2
2
3
3
-
3
+
1
1
-
2
2
2
1
2
3
-
1
-
3
-
1
1
-
2
2
2
1
-
2
3
-
1
3
=
1
-
2
6
-
6
-
2
-
3
+
2
+
2
3
-
2
-
1
1
6
-
6
-
2
-
6
-
6
+
2
6
+
6
+
1
1
-
3
+
2
+
2
-
6
-
6
+
2
-
2
-
3
-
1
1
3
-
2
+
2
6
+
6
+
2
-
2
-
3
=
4
-
48
-
35
-
15
=
-
94
D
1
=
2
1
1
1
-
6
-
2
2
2
-
5
1
-
2
2
-
3
-
1
3
-
3
2
-
2
2
2
1
-
2
2
-
1
3
-
3
-
1
-
6
2
2
-
5
-
2
2
-
3
3
-
3
+
1
-
6
-
2
2
-
5
1
2
-
3
-
1
-
3
-
1
-
6
-
2
2
-
5
1
-
2
-
3
-
1
3
=
2
-
2
6
-
6
-
2
-
3
+
2
+
2
3
-
2
-
1
-
6
6
-
6
-
2
15
+
6
+
2
-
15
-
6
+
1
-
6
-
3
+
2
+
2
15
+
6
+
2
5
+
3
-
1
-
6
3
-
2
+
2
-
15
-
6
+
2
5
+
3
=
188
D
2
=
1
2
1
1
1
-
6
2
2
2
-
5
-
2
2
3
-
3
3
-
3
1
-
6
2
2
-
5
-
2
2
-
3
3
-
3
-
2
1
2
2
2
-
2
2
3
3
-
3
+
1
1
-
6
2
2
-
5
2
3
-
3
-
3
-
1
1
-
6
2
2
-
5
-
2
3
-
3
3
1
-
6
6
-
6
-
2
15
+
6
+
2
-
15
-
6
-
2
1
6
-
6
-
2
-
6
-
6
+
2
6
+
6
+
1
1
15
+
6
+
6
-
6
-
6
+
2
-
6
+
15
-
1
1
-
15
-
6
-
6
6
+
6
+
2
-
6
+
15
=
1
D
3
=
1
1
2
1
1
-
2
-
6
2
2
1
-
5
2
3
-
1
-
3
-
3
1
-
2
-
6
2
1
-
5
2
-
1
-
3
-
3
-
1
1
-
6
2
2
-
5
2
3
-
3
-
3
+
2
1
-
2
2
2
1
2
3
-
1
-
3
-
1
1
-
2
-
6
2
1
-
5
3
-
1
-
3
=
1
-
2
15
+
6
+
6
-
3
+
2
+
2
-
3
-
5
-
1
1
15
+
6
+
6
-
6
-
6
+
2
-
6
+
15
+
2
1
-
3
+
2
+
2
-
6
-
6
+
2
-
2
-
3
-
1
1
-
3
-
5
+
2
-
6
+
15
-
6
-
2
-
3
=
-
141
D
4
=
1
1
1
2
1
-
2
2
-
6
2
1
-
2
-
5
3
-
1
3
-
3
1
-
2
2
-
6
1
-
2
-
5
-
1
3
-
3
-
1
1
2
-
6
2
-
2
-
5
3
3
-
3
+
1
1
-
2
-
6
2
1
-
5
3
-
1
-
3
-
2
1
-
2
2
2
1
-
2
3
-
1
-
3
1
-
2
6
+
15
-
2
-
3
-
5
-
6
3
-
2
-
1
1
6
+
15
-
2
-
6
+
15
-
6
6
+
6
+
1
1
-
3
-
5
+
2
-
6
+
15
-
6
-
2
-
3
-
2
1
-
3
-
2
+
2
-
6
+
6
+
2
-
2
-
3
=
47
Thus
,
x
=
D
1
D
=
188
-
94
=
-
2
y
=
D
2
D
=
-
282
-
94
=
3
z
=
D
3
D
=
-
141
-
94
=
1
.
5
w
=
D
4
D
=
47
-
94
=
-
0
.
5
Suggest Corrections
0
Similar questions
Q.
2x − 3z + w = 1
x − y + 2w = 1
− 3y + z + w = 1
x + y + z = 1
Q.
H
2
(
g
)
+
V
2
O
5
(
s
)
→
V
2
O
3
(
s
)
+
H
2
O
(
l
)
Let the coefficients for the given reaction be as follows:
w
H
2
(
g
)
+
x
V
2
O
5
(
s
)
→
y
V
2
O
3
(
s
)
+
z
H
2
O
(
l
)
What will be the values of w, x, y and z so that the reaction is balanced?
Q.
Solve:
x
−
y
+
z
=
6
;
x
−
2
y
−
2
z
=
5
and
2
x
+
y
−
3
z
=
1
Q.
If
Δ
1
=
∣
∣ ∣
∣
x
−
y
−
z
2
x
2
x
2
y
y
−
z
−
x
2
y
2
z
2
z
z
−
x
−
y
∣
∣ ∣
∣
and
Δ
2
=
∣
∣ ∣
∣
x
+
y
+
2
z
x
y
z
y
+
z
+
2
x
y
z
x
z
+
x
+
2
y
∣
∣ ∣
∣
then
Q.
Solve by matrix method
2
x
+
y
+
2
z
=
5
,
x
−
y
−
z
=
0
,
x
+
2
y
+
3
z
=
5
.
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