Question

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Form a pair of linear equation in two variables using the following information and solve it graphically . (CLASS 10)

➡Five years ago, Sagar was twice as old as Tiru .Ten years later, Sagar's age will be 10 years more than Tiru's age.Find their present ages.


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Answer 1

Answer :-

Statement 1 :-

Five years ago Sagar was twice as old as Tiru .

Statement 2 :-

Ten years later Sagar's age will be 10 years more than Tiru's age .

Now let the present age of

Sagar = x

Tiru = y

Then According to

Statement 1

→ x - 5 = 2(y - 5)

→x - 5 = 2y - 10

→ x = 2y - 5 .....(i)

Statement 2

→ x + 10 = ( y + 10) + 10

→ x + 10 = y + 20

→ x = y + 10 ....(ii)

Now from (i) and (ii)

→ 2y - 5 = y + 10

→ 2y - y = 10 + 5

→ y = 15

Now putting value of y in equation (ii)

→ x = y + 10

→ x = 15 + 10

→ x = 25

So Present age of

Sagar = x = 25 years

Tiru = y = 15 years

Graph :- In graph 1 we will plot line

→ x - 5 = 2y - 10 (green)

When

x | y

________

-5 | 0

-4 | 0.5

-3 | 1

-2 | 1.5

-1 | 2

0 | 2.5

1 | 3

2 | 3.5

3 | 4

→ x + 10 = y + 20 (blue)

x | y

________

-10 | 0

0 | -10

20 | 10

Now we will Mark Point A where Both line intersect

Graph 2 :-

Now we will draw a perpendicular

AB on x-axis

AC on y-axis

The point B will be the value of x

The point C will be the value of y

From graph

x → 25

y → 15

Answer 2

Step-by-step explanation:

Now let the present age of

Sagar = x

Tiru = y

Then According to

Statement 1

→ x - 5 = 2(y - 5)

→x - 5 = 2y - 10

→ x = 2y - 5 .....(i)

Statement 2

→ x + 10 = ( y + 10) + 10

→ x + 10 = y + 20

→ x = y + 10 ....(ii)

Now from (i) and (ii)

→ 2y - 5 = y + 10

→ 2y - y = 10 + 5

→ y = 15

Now putting value of y in equation (ii)

→ x = y + 10

→ x = 15 + 10

→ x = 25

So Present age of

Sagar = x = 25 years

Tiru = y = 15 years

Graph :- In graph 1 we will plot line

→ x - 5 = 2y - 10

When

x | y

________

-5 | 0

-4 | 0.5

-3 | 1

-2 | 1.5

-1 | 2

0 | 2.5

1 | 3

2 | 3.5

3 | 4

→ x + 10 = y + 20

x | y

________

-10 | 0

0 | -10

20 | 10