Question

08. Two years later a father will be eight years more than three times the age of the son. Taking
the present age of father and son as X and Y respectively,
A) Write a linear equation for the above and draw its graph.
B) From the graph find the age of father when son's age is 10 years.​

Answer 1

Step-by-step explanation:

Given :-

Two years later a father will be eight years more than three times the age of the son. Taking

the present age of father and son as X and Y respectively.

To find :-

A) Write a linear equation for the above and draw its graph.?

B) From the graph find the age of father when son's age is 10 years.?

Solution :-

Let the present age of father be X years

Let the present age of son be Y years

Two years later the age of father will be

(X+2) years

Two years later the age of his son = (Y+2) years

According to the given problem

Two years later a father will be eight years more than three times the age of the son.

=> X+2 = 3(Y+2)+8

=> X+2 = 3Y+6+8

=> X+2 = 3Y+14

=> X+2-3Y-14= 0

=> X-3Y-12 = 0

This is the required equation.

=> X = 3Y+12

If we take X = 0,3,6,9... Then we get

Y = -4,-3,-2,-1,0...

The coordinates = (0,-4),(3,-3),(6,-2),(9,-1),(12,0),...

Scale :-

On X -axis 1 Cm = 3 Units

On Y-axis 1 Cm = 2 units

If If Y = 10 then

X = 3(10)+12

=> X = 30+12

=> X = 42

The value of X is 42 when Y = 10

by graph also.

Answer :-

A) The required linear equation in two variables is X-3Y-12 = 0

B) The age of father when the age of son is 10 years is 42 years