Question

How do you graph each system and determine the number of solutions of `x+y=6, x-y=4`?

Answer 1

There is one set of solutions.

Explanation:

Both equations are linear, so there is either one set of solutions, no solutions, or infinite solutions.

In order to graph the system, you can rewrite both equations to a formula form (`y=...`).

`x+y=6harry=-x+6`
`x-y=4harr-y=-x+4harry=x-4`

The graph of the system is equivalent to the graph of both linear formulas:

The lines have one point of intersection, so the system has one set of solutions.