Question

Form a pair of linear equations in two variables using the following information and solve it graphically.

Five years ago, Sita was twice as old as Rema. Ten years later Sita's age will be 10 years more than Rema's age. Find their present ages.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• The present age of Sita be 'x' years.

• The present age of Rema be 'y' years.

Five years ago,

• The age of Sita = x - 5 years

• The age of Rema = y - 5 years.

According to statement,

Sita was twice old as Rema.

$\rm :\longmapsto\:x - 5 = 2(y - 5)$

$\rm :\longmapsto\:x - 5 = 2y -10$

$\rm :\longmapsto\:x - 2y = -10 + 5$

$\bf :\longmapsto\:x - 2y = -5 - - (1)$

Ten years later,

• The age of Sita = x + 10 years

• The age of Rema = y + 10 years.

According to statement,

Sita's age will be 10 years more than Rema's age.

$\rm :\longmapsto\:x + 10 = y + 10 + 10$

$\bf :\longmapsto\:x - y = 10 - - - (2)$

Now, two linear equations are

$\rm :\longmapsto\:x - 2y = - 5 - - - (1)$

and

$\rm :\longmapsto\:x - y = 10 - - - (2)$

Consider equation (1),

$\rm :\longmapsto\:x - 2y = - 5 - - - (1)$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x - 2 \times 0 = - 5$

$\rm :\longmapsto\:x - 0 = - 5$

$\bf\implies \:x = - 5$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0- 2y = - 5$

$\rm :\longmapsto\:- 2y = - 5$

$\rm :\longmapsto\:2y = 5$

$\bf\implies \:y = 2.5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2.5 \\ \\ \sf - 5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 2.5) & (- 5 , 0)

➢ See the attachment graph. [ Red Line ]

Consider

$\rm :\longmapsto\:x - y = 10 - - - (2)$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - y = 10$

$\rm :\longmapsto\: - y = 10$

$\bf\implies \:y = - 10$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x - 0 = 10$

$\bf :\longmapsto\:x = 10$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 10 \\ \\ \sf 10 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 10) & (10 , 0)

➢ See the attachment graph. [ Blue Line ].

So, from graph we conclude that

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Present \: age \: of \: -\begin{cases} &\sf{Sita \: is \: 25 \: years} \\ &\sf{Rema \: is \: 15 \: years} \end{cases}\end{gathered}\end{gathered}$

Answer 2

Answer:

Step-by-step explanation:

Step 1: Form equations using the informations given in the question.

               Let Sagar’s present age be x years

               and Tiru’s present age be y years

               According to the question,

               Condition I:

               Five years ago Sagar was twice as old as Tiru.

               ⇒x−5=2(y−5)

               ⇒x−5=2y−10

               ⇒x−2y=−5.......(i)

               Condition II:

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

               ⇒x+10=(y+10)+10

               ⇒x+10=y+10+10

               ⇒x+10=y+20

               ⇒x−y=10........(ii)

Step 2: Simplify to obtain the required result.

               From eq(i)

               x=2y−5.......(iii)

               Putting the value of x in equation (ii)

               ⇒2y−5−y=10

               ⇒2y−y=10+5

               ⇒y=15

               Putting the value of y in equation (iii)

               ⇒x=2×15−5

               ⇒x=25

Hence, Sagar’s and Tiru’s ages are 25 years and 15 years respectively.