Question

The sum of two numbers is 21. Twice the first number less than the second number is 6. What are the two numbers.​

Answer 1

Step-by-step explanation:

Equation 1)    x + y = 21                                    

                            y = 21 - x    

Equation 2)  2x - y = 6

Solve the system by substitution:

Substitute  21-x for y in Equation 2:

     

        2x - (21-x) = 6

        2x + (-21 + x) = 6      (Change the sign of each term of  the subtrahend,    then add/combine like terms)

        2x + x - 21 = 6

        3x = 6 + 21

        3x/3 = 27/3

        x = 9      

Substitute 9 for x:

  First number: x = 9

  Second number: 21-9 = 12

ANSWER:  The numbers are 9 (first number) and 12 (second number).

Check:

9 + 12 = 21

21 = 21    (True)

2(9) - 12 = 6

18 - 12 = 6

6 = 6  (True)

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