Final answer:
The point (5,8) is not a solution to the system of equations because it only satisfies one of the two equations. For a point to be a solution, it must satisfy all equations in the system.
Step-by-step explanation:
The student asked if the point (5,8) is a solution to the system of equations consisting of 4x + y = 28 and x - y = 3. To justify the response, we will substitute the x-coordinate and y-coordinate of the point (5,8) into both equations to see if they hold true.
For the first equation, 4x + y = 28, substituting (5,8) gives us 4(5) + 8, which equals 20 + 8; hence, our equation becomes 28 = 28, which is true.
For the second equation, x - y = 3, substituting (5,8) gives us 5 - 8, which is -3; therefore, the equation becomes -3 = 3, which is false.
As (5,8) satisfies only one of the two equations, it is not a solution to the system of equations. A point must satisfy all equations within a system to be considered a solution.