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Sol.
Q. Aftab tells his daughter “Seven years ago, I was seven times as old as you were �then. Also, three years from now, I shall be three times as you will be”.
Represent this situation algebraically and graphically.
Aftab
Daughter
Present Age
x years
y years
7 years ago
(x – 7) years
(y – 7) years
(x – 7) =
7 ×
(y – 7)
∴ x – 7 =
7y
– 49
∴ x
– 7y =
– 49
+ 7
∴ x – 7y =
– 42
…….(i)
3 years after
(x + 3) years
(y + 3) years
(x + 3) =
3 ×
(y + 3)
∴ x + 3 =
3y
+ 9
∴ x
– 3y =
9
– 3
∴ x – 3y =
6
…….(ii)
Lets represent given situation algebraically
Sol.
Q. Aftab tells his daughter “Seven years ago, I was seven times as old as you were �then. Also, three years from now, I shall be three times as you will be”.
Represent this situation algebraically and graphically.
x – 7y = – 42
…….(i)
x – 3y = 6
…….(ii)
Lets represent given situation graphically
For graphical representation we need two solutions of each equation
x
y
(x, y)
0
6
(0, 6)
7
7
(7, 7)
x
y
(x, y)
0
- 2
(0, - 2)
6
0
(6, 0)
0 – 7y = – 42
–7y = – 42
y = 6
7 – 7y = – 42
–7y = – 42 – 7
–7y = – 49
y = 7
0 – 3y = 6
–3y = 6
y = –2
6 – 3y = 6
–3y = 6 – 6
–3y = 0
y = 0
1
2
3
4
5
6
0
1
7
(7 , 7)
(0 , 6)
Scale :
1 cm = 1 unit on both the axes
X
Y
x – 7y = –42
x – 3y = 6
3
2
5
4
7
6
(6,0)
8
-1
-2
(0, -2)
-3
-4
-1
-2
-3
-4
Y′
X′