Final Answer:
The solution to the system of equations is (x, y) = (5, 12).
Step-by-step explanation:
To solve the system of equations by substitution, we'll first isolate one variable in one of the equations and then substitute it into the other equation. Let's start with the first equation, \(y + 7 = 2x\), and solve for y.
y = 2x - 7
Now, substitute this expression for y into the second equation 2y = 4x - 14:
2(2x - 7) = 4x - 14
Expand and simplify:
4x - 14 = 4x - 14
As the equation holds true, it means that the system has an infinite number of solutions. The reason for this is that the two equations represent the same line in the xy-plane. Any point on this line is a solution.
Therefore, there is no unique solution in the form of an ordered pair (x, y). This conclusion is reached by substituting the expression for y from the first equation into the second equation, resulting in a true statement that indicates infinitely many solutions.