9.2 Use of Simultaneous Linear Equations
A) Number Problems :
Example Find two numbers whose sum is 70 and difference is 10.
Solution : You are looking for two numbers.
Let the two numbers be x and y. (x > y)
Now we set up two equations from the two conditions given in the problem.
Solving (1) and (2) by adding them
x + y = 70
x - y = 10
\ x = 40
2x = 80
Now, substituting in (1), we get 40 + y = 70 \ y = 30
Therefore, the two numbers are 40 and 30.
Example The difference between two numbers is 8 and 10 times the smaller number and is equal to eight times the greater. Find the smaller number.
Solution : Let the greater number be x and the smaller number be y.
From the given conditions we set two equations as