We are given a system of two linear equations: $5x + y = 14$ $3x - y = 10$ We need to find the solution to this system of equations by graphing. Based on the graphing, we need to choose whether the system has a unique 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 given a system of two linear equations:

$5x + y = 14$

$3x - y = 10$

We need to find the solution to this system of equations by graphing. Based on the graphing, we need to choose whether the system has a unique 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

First, let's rewrite each equation in slope-intercept form ($y = mx + b$).

Equation 1: $5x + y = 14$

Subtract $5x$ from both sides:

$y = -5x + 14$

Equation 2: $3x - y = 10$

Subtract $3x$ from both sides:

$-y = -3x + 10$

Multiply both sides by -1:

$y = 3x - 10$

Now we have the equations in slope-intercept form:

$y = -5x + 14$

$y = 3x - 10$

To find the solution, we set the two equations equal to each other:

$-5x + 14 = 3x - 10$

Add $5x$ to both sides:

$14 = 8x - 10$

Add 10 to both sides:

$24 = 8x$

Divide by 8:

$x = 3$

Now, substitute $x = 3$ into either equation to find $y$. Let's use $y = 3x - 10$:

$y = 3(3) - 10$

$y = 9 - 10$

$y = -1$

Therefore, the solution is $(3, -1)$.

3. Final Answer

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