Respuesta :

altavistard

Answer:

the solution is (40, 21)

Step-by-step explanation:

Let the two numbers be x and y.

Then x + y = the sum = 61, and

         x - y = the difference = 19.

Solve the system of linear equations

x + y = 61

x - y  = 19

Combining these two equations:

x + y = 61

x - y  = 19

---------------

2x    =  80, so x must be 40.

Substituting 40 for x in the first equation, we get 40 + y = 61.  

Combining the constants, we get y = 21.

Then the solution is (40, 21).

The numbers whose sum is 61 and difference 19 are 40 and 21. This is obtained by using algebraic expression for the given condition.

Find the algebraic expression for the question:

Given that sum of numbers is 61 and difference is 19.

Let the larger number be x and smaller number be y.

Then we can write that, x+y=61 (sum) and x-y=19 (difference)

Calculate the numbers:

By solving the algebraic equations we can find the numbers.

  • From second equation we can write, x = 19+y
  • Substitute this in first equation,

(19+y) + y = 61

19+2y = 61

2y = 61 - 19 = 42

y=42/2=21 ⇒ y=21 is the smaller number

x = 19+y = 19+21 =40 ⇒ x=40 is the larger number

Hence the numbers whose sum is 61 and difference 19 are 40 and 21.

Learn more about algebraic expression here:

brainly.com/question/6578178

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