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Byju's Answer
Standard X
Mathematics
Representing Linear Equations for a Word Problem
If 2 x+y+25=3...
Question
If
2
x
+
y
+
2
5
=
3
x
-
y
+
1
3
=
3
x
+
2
y
+
1
6
then
(a) x = 1, y = 1 (b) x = − 1, y = − 1 (c) x = 1, y = 2 (d) x = 2, y = 1
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Solution
Consider
2
x
+
y
+
2
5
=
3
x
-
y
+
1
3
and
3
x
-
y
+
1
3
=
3
x
+
2
y
+
1
6
. Now, simplifying these equations, we get
3
2
x
+
y
+
2
=
5
3
x
-
y
+
1
⇒
6
x
+
3
y
+
6
=
15
x
-
5
y
+
5
⇒
9
x
-
8
y
=
1
.
.
.
.
.
i
And
6
3
x
-
y
+
1
=
3
3
x
+
2
y
+
1
⇒
18
x
-
6
y
+
6
=
9
x
+
6
y
+
3
⇒
3
x
-
4
y
=
-
1
.
.
.
.
.
i
i
Multiplying (ii) by 2 and subtracting it from (i)
9
x
-
6
x
=
1
+
2
⇒
x
=
1
Now, putting x = 1 in (ii), we have
3
×
1
-
4
y
=
-
1
⇒
y
=
3
+
1
4
=
1
Thus, x = 1, y = 1.
Hence, the correct answer is option (a).
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1
Similar questions
Q.
If
29
x
+
37
y
=
103
and
37
x
+
29
y
=
95
then
(a) x = 1, y = 2 (b) x = 2, y = 1 (c) x = 3, y = 2 (d) x = 2, y = 3
Q.
If 2x + 3y = 12 and 3x − 2y = 5 then
(a) x = 2, y = 3 (b) x = 2, y = − 3 (c) x = 3, y = 2 (d) x = 3, y = − 2
Q.
Solve:
x
+
2
y
+
1
2
x
−
y
+
1
=
2
;
3
x
−
y
+
1
x
−
y
+
3
=
5
Q.
Solve the following pairs of equations by reducing them to a pair of linear equations:
(i)
1
2
x
+
1
3
y
=
2
;
1
3
x
+
1
2
y
=
13
6
(ii)
2
√
x
+
3
√
y
=
2
;
4
√
x
−
9
√
y
=
−
1
(iii)
4
x
+
3
y
=
14
;
3
x
−
4
y
=
23
(iv)
5
x
−
1
+
1
y
−
2
=
2
;
6
x
−
1
−
3
y
−
2
=
1
(v)
7
x
−
2
y
x
y
=
5
;
8
x
+
7
y
x
y
=
15
(vi)
6
x
+
3
y
=
6
x
y
;
2
x
+
4
y
=
5
x
y
(vii)
10
x
+
y
+
2
x
−
y
=
4
;
15
x
+
y
−
5
x
−
y
=
−
2
(viii)
1
3
x
+
y
+
1
3
x
−
y
=
3
4
;
1
2
(
3
x
+
y
)
−
1
2
(
3
x
−
y
)
=
−
1
8
Q.
The solution of the equations
3
x
−
y
+
1
3
=
2
x
+
y
+
2
5
=
3
x
+
2
y
+
1
6
given by
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