Questions: Translate the second fact into an equation. Fill in the blanks.

Translate the second fact into an equation. Fill in the blanks.
Transcript text: Translate the second fact into an equation. Fill in the blanks.
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Solution

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Solution Steps

Step 1: Translate the first fact into an equation
  • The first fact states: "One number is six more than a second number."
  • Let x x be the first number and y y be the second number.
  • This translates to: x=y+6 x = y + 6 .
Step 2: Translate the second fact into an equation
  • The second fact states: "Twice the first number is 6 less than 3 times the second number."
  • This translates to: 2x=3y6 2x = 3y - 6 .
Step 3: Solve the system of equations
  • We have two equations:

    1. x=y+6 x = y + 6
    2. 2x=3y6 2x = 3y - 6
  • Substitute x=y+6 x = y + 6 into 2x=3y6 2x = 3y - 6 : 2(y+6)=3y6 2(y + 6) = 3y - 6 2y+12=3y6 2y + 12 = 3y - 6 12+6=3y2y 12 + 6 = 3y - 2y 18=y 18 = y

  • Substitute y=18 y = 18 back into x=y+6 x = y + 6 : x=18+6 x = 18 + 6 x=24 x = 24

Final Answer

  • The first number x x is 24.
  • The second number y y is 18.
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