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Byju's Answer
Standard VII
Mathematics
Types of Brackets
Solve the fol...
Question
Solve the following equations for
(
x
,
y
)
.
2
x
+
y
3
x
−
y
−
x
−
y
x
+
y
=
2
8
15
,
7
x
+
5
y
=
29
A
(
1
,
2
)
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B
(
2
,
3
)
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C
(
−
2
,
3
)
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D
(
4
,
2
)
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Solution
The correct option is
A
(
2
,
3
)
Given equations are
2
x
+
y
3
x
−
y
−
x
−
y
x
+
y
=
2
8
15
..........(1)
and
7
x
+
5
y
=
29
...........(2)
⇒
(
2
x
+
y
)
(
x
+
y
)
−
(
3
x
−
y
)
(
x
−
y
)
(
3
x
−
y
)
(
x
+
y
)
=
38
15
⇒
2
x
2
+
2
x
y
+
x
y
+
y
2
−
3
x
2
+
3
x
y
+
x
y
−
y
2
3
x
2
+
3
x
y
−
x
y
−
y
2
=
38
15
⇒
−
x
2
+
7
x
y
3
x
2
+
2
x
y
−
y
2
=
38
15
⇒
−
15
x
2
+
105
x
y
=
114
x
2
+
76
x
y
−
38
y
2
⇒
129
x
2
−
29
x
y
−
38
y
2
=
0
⇒
129
x
2
−
86
x
y
+
57
x
y
−
38
y
2
=
0
⇒
43
x
(
3
x
−
2
y
)
+
19
y
(
3
x
−
2
y
)
=
0
⇒
(
43
x
+
19
y
)
(
3
x
−
2
y
)
=
0
⇒
43
x
+
19
y
=
0
........(3)
3
x
−
2
y
=
0
..........(4)
Solving (2) and (3), we get
From
(
3
)
y
=
−
43
x
19
Substituting in (2), we get
7
x
+
5
(
−
43
x
19
)
=
29
⇒
x
=
−
581
82
Substituting back in (2)
⇒
y
=
1247
82
So,
(
−
581
82
,
1247
82
)
is one solution of the equation
Similarly by solving (2) and (4), we get
x
=
2
and
y
=
3
So,
(
2
,
3
)
is the other solution of the given equations.
Suggest Corrections
0
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Q.
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x =
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