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Byju's Answer
Standard VI
Mathematics
Solution of an Equation
Solve the fol...
Question
Solve the following simultaneous equations using Cramer’s rule.
(1) 3
x
– 4
y
= 10 ; 4
x
+ 3
y
= 5
(2) 4
x
+ 3
y
– 4 = 0 ; 6
x
= 8 – 5
y
(3)
x
+ 2
y
= –1 ; 2
x
– 3
y
= 12
(4) 6
x
– 4
y
= –12 ; 8
x
– 3
y
= –2
(5) 4
m
+ 6
n
= 54 ; 3
m
+ 2
n
= 28
(6)
2
x
+
3
y
=
2
;
x
-
y
2
=
1
2
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Solution
(1) 3
x
– 4
y
= 10
4
x
+ 3
y
= 5
D
=
3
-
4
4
3
=
3
×
3
-
-
4
×
4
=
9
+
16
=
25
D
x
=
10
-
4
5
3
=
10
×
3
-
-
4
×
5
=
30
+
20
=
50
D
y
=
3
10
4
5
=
3
×
5
-
10
×
4
=
15
-
40
=
-
25
x
=
D
x
D
=
50
25
=
2
y
=
D
y
D
=
-
25
25
=
-
1
x
,
y
=
2
,
-
1
(2) 4
x
+ 3
y
– 4 = 0 ; 6
x
= 8 – 5
y
D
=
4
3
6
5
=
4
×
5
-
6
×
3
=
20
-
18
=
2
D
x
=
4
3
8
5
=
4
×
5
-
3
×
8
=
20
-
24
=
-
4
D
y
=
4
4
6
8
=
4
×
8
-
6
×
4
=
32
-
24
=
8
x
=
D
x
D
=
-
4
2
=
-
2
y
=
D
y
D
=
8
2
=
4
x
,
y
=
-
2
,
4
(3)
x
+ 2
y
= –1 ; 2
x
– 3
y
= 12
D
=
1
2
2
-
3
=
1
×
-
3
-
2
×
2
=
-
3
-
4
=
-
7
D
x
=
-
1
2
12
-
3
=
-
1
×
-
3
-
2
×
12
=
3
-
24
=
-
21
D
y
=
1
-
1
2
12
=
1
×
12
-
-
1
×
2
=
12
+
2
=
14
x
=
D
x
D
=
-
21
-
7
=
3
y
=
D
y
D
=
14
-
7
=
-
2
x
,
y
=
3
,
-
2
(4) 6
x
– 4
y
= –12 ; 8
x
– 3
y
= –2
D
=
6
-
4
8
-
3
=
6
×
-
3
-
-
4
×
8
=
-
18
+
32
=
14
D
x
=
-
12
-
4
-
2
-
3
=
-
12
×
-
3
-
-
4
×
-
2
=
36
-
8
=
28
D
y
=
6
-
12
8
-
2
=
6
×
-
2
-
-
12
×
8
=
-
12
+
96
=
84
x
=
D
x
D
=
28
14
=
2
y
=
D
y
D
=
84
14
=
6
x
,
y
=
2
,
6
(5) 4
m
+ 6
n
= 54 ; 3
m
+ 2
n
= 28
D
=
4
6
3
2
=
4
×
2
-
6
×
3
=
8
-
18
=
-
10
D
x
=
54
6
28
2
=
54
×
2
-
6
×
28
=
108
-
168
=
-
60
D
y
=
4
54
3
28
=
4
×
28
-
54
×
3
=
112
-
162
=
-
50
x
=
D
x
D
=
-
60
-
10
=
6
y
=
D
y
D
=
-
50
-
10
=
5
x
,
y
=
6
,
5
(6)
2
x
+
3
y
=
2
;
x
-
y
2
=
1
2
D
=
2
3
1
-
1
2
=
2
×
-
1
2
-
3
×
1
=
-
1
-
3
=
-
4
D
x
=
2
3
1
2
-
1
2
=
2
×
-
1
2
-
3
×
1
2
=
-
1
-
3
2
=
-
5
2
D
y
=
2
2
1
1
2
=
2
×
1
2
-
2
×
1
=
1
-
2
=
-
1
x
=
D
x
D
=
-
5
2
-
4
=
5
8
y
=
D
y
D
=
-
1
-
4
=
1
4
x
,
y
=
5
8
,
1
4
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25
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Q.
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