To determine the relationship between the two equations, we can analyze them to see if they represent the same line or if they intersect at some point.
The two equations you provided are:
- \( 3x + y = 7 \)
- \( 12x + 4y = 28 \)
Let's first manipulate the second equation to see if it can be simplified.
Starting with the second equation:
\[ 12x + 4y = 28 \]
We can divide the entire equation by 4:
\[ 3x + y = 7 \]
Now we see that the second equation simplifies down to the first equation. This means that both equations represent the same line.
Conclusion:
The two equations are equivalent, meaning they do not intersect at a single point but rather represent an infinite number of points along the same line. Thus, every solution to the first equation is also a solution to the second equation.