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

Jun 23, 2018

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 ($y = \ldots$).

$x + y = 6 \leftrightarrow y = - x + 6$
$x - y = 4 \leftrightarrow - y = - x + 4 \leftrightarrow y = x - 4$

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.