Question

The difference between two numbers is 4. seven times the larger number is 9 times the smaller number. Write a system of equations describing the given conditions. Then solve the system by the substitution method and find the two number

Answer 1

the two numbers are 18 and 14.

Explanation

Let x represent the larger number

y represent the smaller number

x - y = 4. ......... equation 1

7x = 9y. ........ equation 2

from equation 2, solve for x. x= 9y/7

substitute x = 9y/7 into equation 1

9y/7 - y = 4

9y - 7y = 28

2y = 28

y = 28/2

y = 14

Substitute y = 14 into equation 1

x - 14 = 4

x = 4 + 14

x = 18

hence, the larger number is 18 and the smaller number is 14