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Byju's Answer
Standard XII
Mathematics
Consistency of Linear System of Equations
Solve the fol...
Question
Solve the following equation by reduction method:
x
+
3
y
+
3
z
=
16
x
+
4
y
+
4
z
=
21
x
+
3
y
+
4
z
=
19
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Solution
∣
∣ ∣
∣
1
3
3
−
16
1
4
4
−
21
1
3
4
−
19
∣
∣ ∣
∣
R
2
→
R
2
−
R
1
=
∣
∣ ∣
∣
1
3
3
−
16
0
1
0
−
5
1
3
4
−
19
∣
∣ ∣
∣
R
3
→
R
3
−
R
1
=
∣
∣ ∣
∣
1
3
3
−
16
0
1
0
−
5
0
0
1
−
3
∣
∣ ∣
∣
⇒
z
=
−
3
,
y
=
−
5
,
x
+
3
y
+
3
z
=
−
16
⇒
x
+
3
×
−
5
+
3
×
−
3
=
−
16
⇒
x
−
15
−
9
=
−
16
⇒
x
=
−
16
+
24
=
8
∴
x
=
8
,
y
=
−
5
,
z
=
−
3
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