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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThere are two mystery numbers. The sum of 1010 times the first number and 1010 times the second number is −20-20. The sum of 1010 times the first number and 66 times the second number is −4-4. What are the two numbers?\newlineThe first number is _____, and the second number is _____.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThere are two mystery numbers. The sum of 1010 times the first number and 1010 times the second number is −20-20. The sum of 1010 times the first number and 66 times the second number is −4-4. What are the two numbers?\newlineThe first number is _____, and the second number is _____.
  1. Denote Mystery Numbers: Let's denote the first mystery number as xx and the second mystery number as yy. The first equation from the problem statement is 10x+10y=−2010x + 10y = -20. This equation represents the sum of 1010 times the first number and 1010 times the second number.
  2. Form Equations: The second equation from the problem statement is 10x+6y=−410x + 6y = -4. This equation represents the sum of 1010 times the first number and 66 times the second number.
  3. Eliminate Variable: To solve the system using elimination, we need to eliminate one of the variables. We can subtract the second equation from the first to eliminate xx. Subtracting 10x+6y=−410x + 6y = -4 from 10x+10y=−2010x + 10y = -20 gives us 4y=−164y = -16.
  4. Solve for y: Dividing both sides of 4y=−164y = -16 by 44 to solve for yy gives us y=−4y = -4.
  5. Substitute and Solve: Now that we have the value of yy, we can substitute it back into one of the original equations to solve for xx. Let's use the second equation 10x+6y=−410x + 6y = -4. Substituting y=−4y = -4 into this equation gives us 10x+6(−4)=−410x + 6(-4) = -4.
  6. Find xx Value: Simplifying the equation 10x−24=−410x - 24 = -4 by adding 2424 to both sides gives us 10x=2010x = 20.
  7. Find x Value: Simplifying the equation 10x−24=−410x - 24 = -4 by adding 2424 to both sides gives us 10x=2010x = 20. Dividing both sides of 10x=2010x = 20 by 1010 to solve for xx gives us x=2x = 2.

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