Question

fouryears later the father's age will be eight years less than the three times of the age of his son taking the present age of the father and son as X and Y write the linear equation for the information and draw its graph also find the age of the father when the son's age is 10 years old​

Answer 1

Let the present ages of father and son be x yr and y yr, respectively.

Two years later,

Age of father = (x + 2) yr and age of son = (y + 2) yr

According to the question,

Age of father after two years

= 3 (Age of son after two years) + 8

x + 2 = 3(y + 2)+8 =x + 2 = 3y+6+8

x - 3y -12 = 0

which is the required linear equation in two variables.

To draw the graph, we need atleast two solutions of the above equation.

Now, the above equation can be written as

x = 3y +12 ,…(i)

When y = 4,then x = 3x4+12 = 12 +12 =24

When y = 8,then x = 3x8+12 =24+12 = 36

Thus, we have the following table

image

Here, we get the points 4(24, 4) and 6(36, 8). Now, plot the points on the graph paper and join them to get a line AB, which represents the required graph.

image

Now, taking point y=10 on Y axis, draw a line parallel to X-axis, which meets the line at point C and from point C, draw a perpendicular, which intersects X-axis at 42 units distance from Y-axis.

Thus, we get point C(42,10), i.e. when son’s age is 10 yr, then the age of father is 42 yr.

Hope this is helpful to U ✨✨

Good night and have a chocolates dreams ✨