To determine whether $(1, 7)$ is a solution to the system of equations, substitute $x = 1$ and $y = 7$ into both equations:

Equation 1:

$x + 2y = 15$ Substitute $x = 1$ and $y = 7$: $1 + 2(7) = 1 + 14 = 15$ This equation is satisfied.

Equation 2:

$2x + 2y = 16$ Substitute $x = 1$ and $y = 7$: $2(1) + 2(7) = 2 + 14 = 16$ This equation is also satisfied.

Conclusion:

Since both equations are satisfied, $(1, 7)$ is a solution to this system of equations.

Would you like further details or have additional questions? Here are some related queries:

1. What are the steps to graphically solve this system of equations?
2. How can you check if other points are solutions to the system?
3. How would the system behave if the equations were dependent?
4. What does it mean geometrically when a point satisfies a system of equations?
5. Can we solve this system using substitution or elimination methods?

Tip: Always check both equations in the system when verifying a solution.