Question 4 (Multiple Choice Worth 1 points) \( (05.02 \mathrm{MC}) \) Solve the following system of equations: \( \begin{array}{l}x=40+3 y \\ 6 x+13 y=550\end{array} \)

To solve the system of equations, we can substitute the first equation into the second. Start with \( x = 40 + 3y \), then substitute this into the second equation: \[ 6(40 + 3y) + 13y = 550 \] This simplifies to: \[ 240 + 18y + 13y = 550 \] Combining like terms results in: \[ 31y + 240 = 550 \] Next, isolate \( y \): \[ 31y = 550 - 240 \\ 31y = 310 \\ y = 10 \] Now substitute \( y \) back into the first equation to find \( x \): \[ x = 40 + 3(10) \\ x = 40 + 30 \\ x = 70 \] Hence, the solution to the system of equations is \( (x, y) = (70, 10) \). Now, let’s sprinkle in some fun facts! Did you know that systems of equations have been around since ancient civilizations? The Babylonians were among the first to work with these concepts over 4,000 years ago, solving real-world problems such as trade and land distribution using similar methods! For those looking to deepen their understanding, consider exploring resources like Khan Academy or Coursera. They offer interactive courses on algebra and systems of equations, making math feel less daunting and maybe even a bit like a puzzle to solve!