Which pair of equations will have lines meeting at the origin ( (0,0) ) on the graph?

Correct answer: (2x+y=0) and (x-y=0)

A point lies on a line when its coordinates satisfy the equation of that line. Therefore, for two lines to meet at the origin, the coordinates \((0,0)\) must satisfy both equations in the pair. This is a direct substitution test and does not require solving the whole system.

For option B, \(2x+y=0\) gives \(2(0)+0=0\), and \(x-y=0\) gives \(0-0=0\). Thus both lines pass through the origin, so their intersection is at the origin because they are distinct lines. In the other options, at least one equation has a nonzero constant that fails when \(x=y=0\). Hence option B is correct.