Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers.

The sum of two numbers is 75. One number is 23 more than the other. Find the numbers.

The value of two numbers is x=49 and y=26 and the corresponding equation for the given condition is x + y = 75

Explanation:

Given:

Sum of two numbers is 75

One number is 23 more than other

To find:

Frame the equation for the above condition and find the value of two numbers.

Solution:

From the given we know that the sum of two numbers is 75

Let x and y be the numbers, such that the equation is framed as

x + y = 75

And we also know that one number is 23 more than other, so we can say either x or y has a greater one

Here I say x is 23 more than y such that,

x=23+y

Substitute the value of x in the equation and we know

x + y=75 and x=23+y we get,

23+y+y=75

23+2y=75

2y=75-23

2y=52

y=26

Since x=23+y as already stated we get as

x=23+26=49

Result:

Thus the equation for the above given conditions is x + y = 75 and the values of two number is 49 and 26