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Byju's Answer
Standard IX
Mathematics
General Form of a Linear Equation in Two Variables
7 x-5 y=-1 ; ...
Question
7x
-
5y =
-
1; 5x
-
7y =
-
11
Open in App
Solution
7
x
-
5
y
=
-
1
.
.
.
(
i
)
5
x
-
7
y
=
-
11
.
.
.
(
ii
)
Here
we
observe
that
the
coefficients
of
x
and
y
in
the
first
equation
are
interchanged
in
the
second
equation
.
Adding
these
two
equations
,
we get
:
7
x
-
5
y
=
-
1
5
x
-
7
y
=
-
11
12
x
-
12
y
=
-
12
∴
12
x
-
y
=
-
12
∴
x
-
y
=
-
1
.
.
.
(
iii
)
Subtracting
eq
(ii)
from
(i)
,
we get
:
7
x
-
5
y
=
-
1
5
x
-
7
y
=
-
11
-
+
+
2
x
+
2
y
=
10
2
x
+
y
=
10
∴
x
+
y
=
5
.
.
.
(
iv
)
From
(
iii
)
and
(
iv
)
,
we
get
:
x
-
y
=
-
1
and
x
+
y
=
5
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0
Similar questions
Q.
Find the values of the
x
+
y
and
x
−
y
from the examples given below without solving for x and y
7
x
−
5
y
=
−
1
;
5
x
−
7
y
=
−
11
Q.
The equation of the obtuse angle bisector of lines
12
x
−
5
y
+
7
=
0
and
3
y
−
4
x
−
1
=
0
is
Q.
Prove that,
cos
(
7
x
−
5
y
)
+
cos
(
7
y
−
5
x
)
sin
(
7
x
−
5
y
)
+
sin
(
7
y
−
5
x
)
=
cot
(
x
+
y
)
.
Q.
Prove that
cos
(
7
x
−
5
y
)
+
cos
(
7
y
−
5
x
)
sin
(
7
x
−
5
y
)
+
sin
(
7
y
−
5
x
)
=
cot
(
x
+
y
)
Q.
5
x
+
7
y
=
9
and
7
x
+
5
y
=
21
, then what is the value of
x
−
y
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