Questions: Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, has no solution, or has an infinite number of solutions. If the system has one solution, find the solution. y=8x-13 y=8x+17

Solution Steps

To solve the given system of linear equations by addition, we first observe that both equations have the same slope but different y-intercepts. This indicates that the lines are parallel and will never intersect, meaning there is no solution to the system.

The given system of linear equations is: \[ \begin{align_} y &= 8x - 13 \quad (1) \\ y &= 8x + 17 \quad (2) \end{align_} \]

Both equations have the same slope of \(8\). This indicates that the lines represented by these equations are parallel.

The y-intercepts of the equations are \(-13\) for equation (1) and \(17\) for equation (2). Since the y-intercepts are different, the lines will never intersect.

Since the lines are parallel and do not intersect, the system of equations has no solution.

Final Answer