Question: (See Example 1.) 3. \((2, 6)\); \(x + y = 8\) \(3x - y = 0\)

(See Example 1.)

3. \((2, 6)\); \(x + y = 8\)

\(3x - y = 0\)

Solution

The problem involves a system of equations and a point to verify: 1. \(x + y = 8\) 2. \(3x - y = 0\) Given point: \((2, 6)\). Let’s verify if the point is a solution to the system: First, substitute \(x = 2\) and \(y = 6\) into the first equation: \[ x + y = 8 \] \[ 2 + 6 = 8 \] \[ 8 = 8 \] The first equation is satisfied. Now, substitute \(x = 2\) and \(y = 6\) into the second equation: \[ 3x - y = 0 \] \[ 3(2) - 6 = 0 \] \[ 6 - 6 = 0 \] \[ 0 = 0 \] The second equation is also satisfied. Therefore, the point \((2, 6)\) is a solution to the system of equations.