To create a consistent and dependent system with the equation x + y = 2, we need to find a second equation that is essentially a multiple of the first one. This means that the two equations represent the same line on a graph.
For instance, if we take the original equation and multiply it by a non-zero constant, we’ll still describe the same line. A good choice could be:
2x + 2y = 4
The reason is that if we multiply the entire equation x + y = 2 by 2, we receive:
2(x + y) = 2(2)
which simplifies to:
2x + 2y = 4
Both equations represent the same line in a two-dimensional plane, thus they will have infinitely many solutions together, creating a consistent and dependent system. A consistent system is one that has at least one solution, and a dependent system is one where there are infinitely many solutions because the equations are multiples of one another.