Answer
The system of equations is dependent so it has infinitely many solutions.
The solution set is: $\left\{\left(\dfrac{6-2y}{7}, y\right)\right\}$.
Work Step by Step
We need to solve the given system of equations:
$$7x+2y=6 ~~~(1) \\ 14x+4y=12 ~~~(2)$$
Multiply first equation by $-2$ and then first equation is equivalent to: $-14x-4y=-12 ~~~~(3)$
Add equations (2) and (3) to eliminate $x$ .
$$14x+4y+(-14x-4y)=12+(-12) \\ 0=0 $$
Both variables were eliminated and resulted in a true equation/statement.
This implies that the system of equations is dependent and has infinitely many solutions, and that the equatoins refer to the same line.
Isolate $x$ from first equation to obtain:
$$7x=6-2y\\
x=\dfrac{6-2y}{7}$$
Thus, the solution set is: $\left\{\left(\dfrac{6-2y}{7}, y\right)\right\}$.