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Linear Equations In Two Variables
NCERT Solutions
NCERT Solutions
Linear Equations In Two Variables
6 Solutions
Exercise:
All Exercises
EXERCISE 4.1
EXERCISE 4.2
Q1
EXERCISE 4.1
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹
x
x
x
and that of a pen to be ₹
y
y
y
).
Q2
EXERCISE 4.1
Express the following linear equations in the form
a
x
+
b
y
+
c
=
0
a x+b y+c=0
a
x
+
b
y
+
c
=
0
and indicate the values of
a
,
b
a, b
a
,
b
and
c
c
c
in each case:
(i)
2
x
+
3
y
=
9.3
5
‾
2 x+3 y=9.3\overline{5}
2
x
+
3
y
=
9.3
5
(ii)
x
−
y
5
−
10
=
0
x-\frac{y}{5}-10=0
x
−
5
y
−
10
=
0
(iii)
−
2
x
+
3
y
=
6
-2 x+3 y=6
−
2
x
+
3
y
=
6
(iv)
x
=
3
y
x=3 y
x
=
3
y
(v)
2
x
=
−
5
y
2 x=-5 y
2
x
=
−
5
y
(vi)
3
x
+
2
=
0
3 x+2=0
3
x
+
2
=
0
(vii)
y
−
2
=
0
y-2=0
y
−
2
=
0
(viii)
5
=
2
x
5=2 x
5
=
2
x
Q1
EXERCISE 4.2
Which one of the following options is true, and why?
y
=
3
x
+
5
y=3 x+5
y
=
3
x
+
5
has
(i)
a unique solution,
(ii)
only two solutions,
(iii)
infinitely many solutions
Q2
EXERCISE 4.2
Write four solutions for each of the following equations:
(i)
2
x
+
y
=
7
2 x+y=7
2
x
+
y
=
7
(ii)
π
x
+
y
=
9
\pi x+y=9
π
x
+
y
=
9
(iii)
x
=
4
y
x=4 y
x
=
4
y
Q3
EXERCISE 4.2
Check which of the following are solutions of the equation
x
−
2
y
=
4
x-2 y=4
x
−
2
y
=
4
and which are not:
(i)
(
0
,
2
)
(0,2)
(
0
,
2
)
(ii)
(
2
,
0
)
(2,0)
(
2
,
0
)
(iii)
(
4
,
0
)
(4,0)
(
4
,
0
)
(iv)
(
2
,
4
2
)
(\sqrt{2}, 4 \sqrt{2})
(
2
,
4
2
)
(v)
(
1
,
1
)
(1,1)
(
1
,
1
)
Q4
EXERCISE 4.2
Find the value of
k
k
k
, if
x
=
2
,
y
=
1
x=2, y=1
x
=
2
,
y
=
1
is a solution of the equation
2
x
+
3
y
=
k
2 x+3 y=k
2
x
+
3
y
=
k
.
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