We are asked to solve the following system of equations: $5x + y = 14$ $2x - y = 7$ We need to determine if the system has a solution, infinitely many solutions, or no solution. If there is a unique solution, we need to provide the ordered pair $(x, y)$.

1. Problem Description

We are asked to solve the following system of equations:

$5x + y = 14$

$2x - y = 7$

We need to determine if the system has a solution, infinitely many solutions, or no solution. If there is a unique solution, we need to provide the ordered pair $(x, y)$.

2. Solution Steps

We can solve this system of equations using the elimination method. Add the two equations together:

$(5x + y) + (2x - y) = 14 + 7$

$7x = 21$

$x = \frac{21}{7}$

$x = 3$

Now, substitute the value of $x$ into the first equation to solve for $y$:

$5(3) + y = 14$

$15 + y = 14$

$y = 14 - 15$

$y = -1$

So, the solution is $x = 3$ and $y = -1$. Therefore, the ordered pair is $(3, -1)$.

To check the solution, substitute $x = 3$ and $y = -1$ into the second equation:

$2(3) - (-1) = 7$

$6 + 1 = 7$

$7 = 7$

The solution is correct.

3. Final Answer

The solution to this system is $(3, -1)$.