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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineDarnel has been planting young trees in her garden. The maple tree that is 5757 centimeters tall is growing 77 centimeters per month, whereas the oak tree that is 6363 centimeters tall is growing 55 centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?\newlineThe two trees will both be _\_ centimeters tall in _\_ months.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineDarnel has been planting young trees in her garden. The maple tree that is 5757 centimeters tall is growing 77 centimeters per month, whereas the oak tree that is 6363 centimeters tall is growing 55 centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?\newlineThe two trees will both be _\_ centimeters tall in _\_ months.
  1. Introduction: Let xx represent the number of months, and yy represent the height of the trees in centimeters after xx months.\newlineFor the maple tree:\newlineInitial height: 5757 centimeters\newlineGrowth rate per month: 77 centimeters/month\newlineEquation based on the given information:\newlineHeight after xx months = initial height + (growth rate * number of months)\newliney=7x+57y = 7x + 57\newlineFor the maple tree, the equation is: y=7x+57y = 7x + 57
  2. Maple Tree Information: For the oak tree:\newlineInitial height: 6363 centimeters\newlineGrowth rate per month: 55 centimeters/month\newlineEquation based on the given information:\newlineHeight after xx months = initial height + (growth rate * number of months)\newliney=5x+63y = 5x + 63\newlineFor the oak tree, the equation is: y=5x+63y = 5x + 63
  3. Oak Tree Information: System of equations:\newliney=7x+57y = 7x + 57\newliney=5x+63y = 5x + 63\newlineTo find the point where the trees are the same height, set the two equations equal to each other:\newline7x+57=5x+637x + 57 = 5x + 63
  4. System of Equations: Solve for xx:\newlineSubtract 5x5x from both sides of the equation:\newline7x+57−5x=5x+63−5x7x + 57 - 5x = 5x + 63 - 5x\newline2x+57=632x + 57 = 63\newlineNow, subtract 5757 from both sides:\newline2x+57−57=63−572x + 57 - 57 = 63 - 57\newline2x=62x = 6\newlineDivide both sides by 22 to isolate xx:\newline2x2=62\frac{2x}{2} = \frac{6}{2}\newline5x5x00
  5. Solving for x: Find the value of yy by substituting xx into one of the system of equations:\newlineSubstitute 33 for xx in y=7x+57y = 7x + 57:\newliney=7(3)+57=21+57=78y = 7(3) + 57 = 21 + 57 = 78\newlineSo, y=78y = 78

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