Answer:
B. No solution.
Step-by-step example
I will try to solve your system of equations.
3x−y=4;6x−2y=7
Step: Solve3x−y=4for y:
3x−y+−3x=4+−3x(Add -3x to both sides)
−y=−3x+4
−y
−1
=
−3x+4
−1
(Divide both sides by -1)
y=3x−4
Step: Substitute3x−4foryin6x−2y=7:
6x−2y=7
6x−2(3x−4)=7
8=7(Simplify both sides of the equation)
8+−8=7+−8(Add -8 to both sides)
0=−1
Therefore, there is no solution, and the lines are parallel.