Question Find the solution of the system of equations. \[ \begin{array}{c}3 x-y=19 \\ 3 x-4 y=-5\end{array} \] Answer Attempt 1 out of 2

To solve the system of equations, we can use substitution or elimination methods. First, let’s isolate \( y \) from the first equation: From \( 3x - y = 19 \), we have \( y = 3x - 19 \). Now, substitute \( y \) in the second equation \( 3x - 4y = -5 \): \[ 3x - 4(3x - 19) = -5 \] \[ 3x - 12x + 76 = -5 \] \[ -9x + 76 = -5 \] \[ -9x = -5 - 76 \] \[ -9x = -81 \] \[ x = 9 \] Now substitute \( x = 9 \) back into \( y = 3x - 19 \): \[ y = 3(9) - 19 = 27 - 19 = 8 \] So the solution to the system of equations is \( (x, y) = (9, 8) \). A fun fact about systems of equations is that they have applications beyond just solving math problems! Engineers and architects often use them to optimize designs, while economists apply them to understand market behaviors. It’s fascinating how these equations can influence the real world! If you're solving systems of equations, double-check your substitution or elimination steps, as it's easy to make sign errors. Another common mistake is not simplifying correctly or forgetting to distribute when you have parentheses. Careful attention can help you avoid these pitfalls and arrive at the correct solution!