Question

represent any 5 day to day problems in the form of linear equations in two variables.also represent them graphically​

Answer 1

Problem statement

If two no. Are in ratio 2:5 and difference between the square of these no. Is 789 then find the number

Solution.

Let x and y be two numbers such that

        x : y = 2 : 5

⇒        x/y = 2/5

⇒           x = 2y/5

Then

According to second condition of question

      y² - x² = 789

Putting x = 2y/5 we get

      y² - (2y/5)² = 789

⇒   y² - 4y²/25 = 789

⇒    25y² - 4y² = 19725

⇒    25y² - 4y² = 19725

                21y² = 19725

                    y² = 19725/21

                      y = √(19725/21)

Putting y = √(19725/21) in x = 2y/5 we get

   x = 2( √(19725/21) ) / 5 = 2√(19725/(21×25)) = 2√(789/21)

So

x = 2√(789/21)

y = √(19725/21)

Checking

x/y =  2√(789/21) /√(19725/21) = (2( √(19725/21) ) / 5) / √(19725/21) = 2 /5

y² - x² = (√(19725/21))² - (2√(789/21))² = 789.

Note

I wrote a single problem and solve them you can find similar cases easily.

Graph is given below.

Intersection of both graphs is the solution.So there are two possibilities but we are interested in positive solution.