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the sum of two numbers is 45. the greater number is 9 more than the other number. Find each number. use a system of linear equations to justify your answer

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Answer:

18 and 27

Step-by-step explanation:

Let x = first (smaller) number

Let y = second (larger) number

Sum of two numbers is 45:

⇒ x + y = 45

The greater number is 9 more than the other number:

⇒ y = x + 9

Substitute  y = x + 9  into  x + y = 45  and solve for x:

⇒ x + (x + 9) = 45

⇒ 2x + 9 = 45

⇒ 2x = 36

⇒ x = 18

Substitute found value for x into  y = x + 9  and solve for y:

⇒ y = 18 + 9

⇒ y = 27

Therefore, the two numbers are 18 and 27

Solution:

Let x and y be the numbers that sum up to 45.

Note that:

  • x + y = 45
  • y + 9 = x

Simplify the second equation such that the constant is the subject.

  • y + 9 = x
  • => -x + y = -9

Use system of equations to solve for both variables.

  • x + y = 45

       -x + y = -9

  • => 2y = 36
  • => y = 18

Substitute the value of y into the second equation to find x.

  • y + 9 = x
  • => 18 + 9 = x
  • => 27 = x

The value of x and y is 27 and 18 respectively.

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