2. Determine which of the following pair of equations are equivalent.
a) X-5 = 9, 2x - 8 = 3x + 6
c) 5x + 2 = 2x + 5, X-9 = 1-9
b) 3y + 7 = y + 5, y - 7 = 1-3y
Answers
Answer:
the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product
Step-by-step explanation:
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Step-by-step explanation:
Solution
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(i)
2x
1
+
3y
1
=2
3x
1
+
2y
1
=
6
13
Lets assume
x
1
=p and
y
1
=q, both equations will become
2
p
+
3
q
=2
⇒3p+2q=12 ... (A)
3
p
+
2
q
=
6
13
⇒2p+3q=13 ...(B)
Multiply (A) by 3 and (B) by 2, we get
9p+6q=36
4p+6q=26
Subtracting these both, we get
5p=10
⇒p=2
⇒x=
p
1
=
2
1
∴q=
6
26−8
=3
⇒y=
q
1
=
3
1
(ii)
x
2
+
y
3
=2
x
4
−
y
9
=−1
Lets assume
x
1
=p and
y
1
=q, both equations will become
2p+3q=2 ...(A)
4p−9q=−1 ...(B)
Multiply (A) by 3, we get
6p+9q=6
4p−9q=−1
Adding these both, we get
10p=5
⇒p=
2
1
⇒ x=
p
2
1
=4
∴q=
3
1
⇒y=
q
2
1
=9
(iii)
x
4
+3y=14
x
3
−4y=23
Lets assume
x
1
=p, both equations become
4p+3y=14 ...(A)
3p−4y=23 ...(B)
Multiply (A) by 4 and (B) by 3, we get
16p+12y=56
9p−12y=69
Adding these both, we get
25p=125
⇒p=5
⇒x=
p
1
=
5
1
⇒y=−2
(iv)
x−1
5
+
y−2
1
=2
x−1
6
−
y−2
3
=1
Lets assume
x−1
1
=p and
y−2
1
=q, both equations become
5p+q=2
6p−3q=1
Multiply (A) by 3, we get
15p+3q=6
6p−3q=1
Adding both of these, we get
21p=7
⇒p=
3
1
⇒ x=4
∴q=
3
1
⇒ y=5
(v)
xy
7x−2y
=5
⇒
y
7
−
x
2
=5
xy
8x+7y
=15
⇒
y
8
+
x
7
=15
Let t=
x
1
and r=
y
1
equation will be
7r−2t=5;8r+7t=15
On solving we get
t=1r=1
∴x=1andy=1
(vi)
Dividing both side by xy then we have
y
6
+
x
3
=6;
y
2
+
x
4
=5
Let t=
x
1
andr=
y
1
equation will be
6r+3t=6;2r+4t=5 on solving we get
t=1r=
2
1
∴x=1andy=2
(vii)
Let t=
x+y
1
andr=
x−y
1
then equation will be
10t+2r=4;15t−5r=−2 on solving we have
t=
5
1
andr=1
∴x+y=5andx−y=1
Hence, x=4,y=1
(viii)
Let t=
3x+y
1
andr=
3x−y
1
then equation will be
t+r=
4
3
;
2
t
−
2
r
=
8
−1
On solving we have
t=
4
1
andr=
2
1
∴3x+y=4and3x−y=2
Hence, x=1,y=1