when would we say that the relationship between two variables x and y is spurious
Spurious relationship In statistics, a spurious relationship or spurious correlation[1][2] is a mathematical relationship in which two or more events or variables are not causally related to each other, yet it may be wrongly inferred that they are, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or "lurking variable").
Consistent and inconsistent equations In mathematics and in particular in algebra, a linear or nonlinear system of equations is consistent if there is at least one set of values for the unknowns that satisfies every equation in the systemâ€”that is, that when substituted into each of the equations makes each equation hold true as an identity. In contrast, an equation system is inconsistent if there is no set of values for the unknowns that satisfies all of the equations.