This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the equation of the line passing through the intersection of the lines \(x + y = 5\) and \(2x - y - 7 = 0\), and parallel to the x-axis, follow these steps: 1. Find the intersection point of the two lines: From \(x + y = 5\), we can express \(y\) as \(y = 5 - x\). Substitute \(y\) into the second equation: \[ 2x - (5 - x) - 7 = 0 2x - 5 + x - 7 = 0 3x - 12 = 0 x = 4. \] Substitute \(x = 4\) back into \(y = 5 - x\): \[ y = 5 - 4 = 1. \] The intersection point is \((4, 1)\). 2. Equation of the line parallel to the x-axis: A line parallel to the x-axis has the form \(y = k\), where \(k\) is a constant. Since the line must pass through the point \((4, 1)\), the equation is: \[ y = 1. \] Thus, the equation of the line is \(y = 1\).