Question

Construct a word problem on a simultaneous linear equation in two variables so that the value of one of the variables will be 10 (persons, rupees, meters, years etc.) and solve it.

Answer 1

Hint: Two linear equations in two variables taken together are called simultaneous linear equations. The solution of a system of simultaneous linear equations is the ordered pair (x,y). which satisfies both the linear equations.

Complete step by step solution:
Step1: From a bus stand in Chandigarh, if we buy 2 tickets to zirakpur and 3 tickets to rajpura, the total cost is Rs. 46; but If we buy 3 tickets to zirakpur and 5 tickets to Rajpura, the total cost is Rs. 74. Find the fares from the bus stand to Zirakpur to Rajpura.
Step2: Let Rs. X be the fare from the bus stand in Chandigarh to zirakpur, and Rs. to rajpura.
From the given information, we have
$
  2x + 3y = 36 \\
  3x + 5y = 74 \\
 $ i.e. . $
  2x + 3y - 36 = 0 \\
  3x + 5y - 74 = 0 \\
 $
Step 3: To solve the equations by the cross multiplication method. We can draw the diagram as given below

Then \[\dfrac{x}{{(3)( - 74) - (5)( - 46)}} = \dfrac{y}{{( - 46)(3) - ( - 74)(2)}} = \dfrac{1}{{(2)(5) - (3)(3)}}\]
i.e. \[\dfrac{x}{{ - 222 + 230}} = \dfrac{y}{{ - 138 + 148}} = \dfrac{1}{{10 - 9}}\]
 i.e. \[\dfrac{x}{8} = \dfrac{y}{{10}} = \dfrac{1}{1}\]
i..e. \[\dfrac{x}{8} = \dfrac{1}{1}\] and \[\dfrac{y}{{10}} = \dfrac{1}{1}\]
∴ \[x = 8\] and \[y = 10\]

Hence, the fare from the bus stand in Chandigarh to zirakpur is Rs. 8 and the fare to Rajpura is Rs. 10

Note:
To remember how to solve the simultaneous equation by use of following methods
1. Method of comparison:- Method comparison measures the closeness of agreement between the measured values of two methods.
2. Method of cross multiplication:- In Maths, cross multiplication method is used to solve linear equations in two variables. This is the simplest method and gives the accurate value of the variables.