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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineMr. Buckley is contemplating which chauffeured car service to take to the airport. The first costs $4\$4 up front and $2\$2 per kilometer. The second costs $20\$20 plus $1\$1 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?\newlineFor a driving distance of __\_\_ kilometers, the total fare is $__\$\_\_.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineMr. Buckley is contemplating which chauffeured car service to take to the airport. The first costs $4\$4 up front and $2\$2 per kilometer. The second costs $20\$20 plus $1\$1 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?\newlineFor a driving distance of __\_\_ kilometers, the total fare is $__\$\_\_.
  1. Define Equations: Step 11: Define the equations for the total fare from each service.\newlineFor the first service: Total fare = $4\$4 + $2\$2 per kilometer.\newlineLet xx be the number of kilometers, then the equation is y=2x+4y = 2x + 4.\newlineFor the second service: Total fare = $20\$20 + $1\$1 per kilometer.\newlineThe equation is y=x+20y = x + 20.
  2. Set Equations Equal: Step 22: Set the equations equal to solve for xx using substitution.2x+4=x+202x + 4 = x + 20Subtract xx from both sides: 2x−x=20−42x - x = 20 - 4x=16x = 16
  3. Substitute and Solve: Step 33: Substitute x=16x = 16 back into either equation to find yy, the total fare.\newlineUsing the first service's equation: y=2(16)+4y = 2(16) + 4\newliney=32+4y = 32 + 4\newliney=36y = 36

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