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Byju's Answer
Standard IX
Mathematics
Solving Simultaneous Linear Equations by Graphical Method
Q Find the eq...
Question
Q Find the equation of the line passing through the intersection of the lines 4x+3y=1 and 5x+4y=2 and
i) parallel to the line x+2y-5=0
ii) perpendicular to x-axis.
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Solution
Dear student
The
intersection
of
the
line
4
x
+
3
y
=
1
.
.
.
1
and
5
x
+
4
y
=
2
.
.
.
2
can
be
find
by
solving
the
two
equations
simultaneously
.
Multiply
1
by
5
and
2
by
4
.
20
x
+
15
y
=
5
.
.
.
3
20
x
+
16
y
=
8
.
.
.
4
Subtracting
3
from
4
,
we
get
20
x
+
16
y
-
20
x
-
15
y
=
8
-
5
y
=
3
Putting
in
1
,
we
get
4
x
+
3
3
=
1
4
x
=
-
8
x
=
-
2
Thus
,
the
point
of
intersection
of
two
lines
is
-
2
,
3
This
point
lies
on
the
required
line
.
i
Slope
of
line
y
=
mx
+
c
is
m
.
The
slope
of
the
required
line
is
same
as
that
of
line
∵
when
two
lines
are
∥
,
their
slopes
are
equal
.
x
+
2
y
-
5
=
0
2
y
=
-
x
+
5
y
=
-
1
2
x
+
5
2
Thus
,
the
slope
of
line
is
-
1
2
So
,
equation
of
the
required
line
is
y
-
y
1
=
m
x
-
x
1
where
m
is
the
slope
and
x
1
,
y
1
=
-
2
,
3
is
a
point
on
line
.
Thus
,
equation
of
required
line
is
:
y
-
3
=
-
1
2
x
-
-
2
y
-
3
=
-
1
2
x
+
2
2
y
-
6
=
-
x
-
2
x
+
2
y
-
4
=
0
ii
⊥
to
x
axis
.
Equation
of
line
⊥
to
x
axis
is
given
by
x
=
k
,
where
k
is
a
constant
-
2
,
3
lies
on
the
line
x
=
k
given
So
,
k
=
-
2
Thus
,
the
equation
of
straight
line
is
x
=
-
2
or
x
+
2
=
0
Regards
Suggest Corrections
0
Similar questions
Q.
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The equation of the straight line which passes through the intersection of the lines
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Q.
Find the equation of the line passing through the point of intersection of the lines
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