Consider the given system of equations where \( m \) and \( q \) are the slopes of the lines representer \( \left\{\begin{array}{l}y=m x+2 \\ y=q x+8\end{array}\right. \) The solution to the system of equations is the ordered pair \( (2,3) \)

To find the values of \( m \) and \( q \) in the given system of equations, we can substitute the ordered pair \( (2,3) \) into the equations and solve for \( m \) and \( q \). Given system of equations: \[ y = mx + 2 \] \[ y = qx + 8 \] Substitute the ordered pair \( (2,3) \) into the equations: \[ 3 = 2m + 2 \] \[ 3 = 2q + 8 \] Now, we can solve these equations to find the values of \( m \) and \( q \). Solve the equation by following steps: - step0: Solve for \(m\): \(3=2m+2\) - step1: Swap the sides: \(2m+2=3\) - step2: Move the constant to the right side: \(2m=3-2\) - step3: Subtract the numbers: \(2m=1\) - step4: Divide both sides: \(\frac{2m}{2}=\frac{1}{2}\) - step5: Divide the numbers: \(m=\frac{1}{2}\) Solve the equation \( 3 = 2q + 8 \). Solve the equation by following steps: - step0: Solve for \(q\): \(3=2q+8\) - step1: Swap the sides: \(2q+8=3\) - step2: Move the constant to the right side: \(2q=3-8\) - step3: Subtract the numbers: \(2q=-5\) - step4: Divide both sides: \(\frac{2q}{2}=\frac{-5}{2}\) - step5: Divide the numbers: \(q=-\frac{5}{2}\) The values of \( m \) and \( q \) are \( m = 0.5 \) and \( q = -2.5 \) respectively.