Given the system of equations, what is the \( x \)-coordinate of the solution? \( \begin{array}{l}y=3-\frac{1}{2} x \\ 3 x+4 y=1 \\ -17 / 2 \\ -11\end{array} \)
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Bonus Knowledge
To find the \( x \)-coordinate of the solution, we can start by substituting \( y \) from the first equation into the second equation. 1. From the first equation: \[ y = 3 - \frac{1}{2} x \] 2. Substitute for \( y \) in the second equation: \[ 3x + 4(3 - \frac{1}{2} x) = 1 \] 3. Now simplify the equation: \[ 3x + 12 - 2x = 1 \] \[ x + 12 = 1 \] \[ x = 1 - 12 \] \[ x = -11 \] So, the \( x \)-coordinate of the solution is \( -11 \).
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