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Miguel and his mom are planting vegetables in their garden. Miguel has finished planting 11 row of carrots so far and is planting new rows at a rate of 44 rows per hour. His mom has finished 77 rows of tomatoes and will continue planting at 11 row per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed?\newlineWrite a system of equations, graph them, and type the solution.\newline____ rows\newline

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Q. Miguel and his mom are planting vegetables in their garden. Miguel has finished planting 11 row of carrots so far and is planting new rows at a rate of 44 rows per hour. His mom has finished 77 rows of tomatoes and will continue planting at 11 row per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed?\newlineWrite a system of equations, graph them, and type the solution.\newline____ rows\newline
  1. Define Variables and Equations: Define the variables and write the equations for Miguel and his mom's planting rates. Miguel has already planted 11 row and plants 44 more rows per hour. His mom has already planted 77 rows and plants 11 more row per hour. Let tt be the time in hours after which they will have planted the same number of rows.\newlineMiguel's rows: 1+4t1 + 4t\newlineMom's rows: 7+t7 + t
  2. Set Equations Equal: Set the equations equal to find the time when they have the same number of rows. \newline1+4t=7+t1 + 4t = 7 + t
  3. Solve for tt: Solve for tt by isolating tt on one side.\newline1+4tt=71 + 4t - t = 7\newline3t=63t = 6\newlinet=2t = 2
  4. Substitute t and Find Rows: Substitute t=2t = 2 back into either equation to find the number of rows each has completed.\newlineUsing Miguel's equation: 1+4(2)=1+8=91 + 4(2) = 1 + 8 = 9

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