EXERCISE 3.1
1. Aftab tells his daughter, "Seven years ago, I was seven times as old as you were the
Also, three years from now, I shall be three times as old as you will be." (Isn't thi
2. The coach of a cricket team buys 3 bats and 6 balls for 3900. Later, she buys another
bat and 3 more balls of the same kind for 1300. Represent this situation algebraical
3. The cost of 2 kg of apples and lkg of grapes on a day was found to be 160. After
month, the cost of 4 kg of apples and 2 kg of grapes is 300. Represent the situatic
next fes
how these representations can be
used to look for solutions of the pair
of linear equations
Fig. 3.4
interesting?) Represent this situation algebraically and graphically.
and geometrically
algebraically and geometrically.
3 Graphical Method of Solution of a pair of Linear Equations
the previous section, you have seen how we can graphically represent a pair
Answers
HEY MATE,HERE'S UR ANSWER........
Consider Aftab's age as x and his daughter's age as y.
Then , seven years ago,
Aftab's age =x−7
His daughter's age =y−7
According to the question,
x−7=7(y−7)
x−7=7y−49
x−7y=−49+7
x−7y=−42 …(i)
After three years,
Aftab's age =x+3
His daughter's age =y+3
According to the question,
x+3=3(y+3)
x+3=3y+9
x−3y=9−3
x−3y=6 …(ii)
Representing equation (i) and (ii) geometrically, we plot these equations by finding points on the lines representing these two equations
x−7y=−42⟹x=7y−42
x=7y−42 42 35 49
y 12 11 13
x−3y=6⟹x=3y+6
x=3y+6 42 36 48
y 12 10 14
From the graph we can see that two lines will intersect at a point.
x−7y=−42
x−3y=6
On subtracting the two equations, we get
4y=48
or y=12
Substituting value of y in (2),
x−36=6
∴x=42
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