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Byju's Answer
Standard X
Mathematics
Cross-Multiplication Method of Finding Solution of a Pair of Linear Equations
Solve the fol...
Question
Solve the following systems of equations by the method of cross-multiplication:
5
x
+
y
−
2
x
−
y
=
−
1
15
x
+
y
+
7
x
−
y
=
10
where
x
≠
0
,
y
≠
0
and
x
≠
y
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Solution
Substitute
1
x
+
y
=
a
and
1
x
−
y
=
b
We get equations as follows:
5
a
−
2
b
+
1
=
0
and
15
a
+
7
b
−
10
=
0
Using method of cross-multiplication we get:
a
(
−
2
)
(
−
10
)
−
(
7
)
(
1
)
=
b
(
1
)
(
15
)
−
(
−
10
)
(
5
)
=
1
(
5
)
(
7
)
−
(
15
)
(
−
2
)
a
13
=
b
65
=
1
65
From
a
13
=
1
65
we get
a
=
1
5
Similarly
b
=
1
Resubstituting values of
a
and
b
we get
x
+
y
=
5
and
x
−
y
=
1
Adding these 2 equations gives us
x
=
3
.
Substracting 2nd equation from 1st gives us
y
=
2
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Similar questions
Q.
Solve each of the following systems of equations by the method of cross-multiplication :
5
x
+
y
-
2
x
-
y
=
-
1
15
x
+
y
+
7
x
-
y
10
,
where x ≠ 0 and y ≠ 0