# Algebra: Graphical Solutions

On this page we hope to clear up problems that you might have with using graphs to find solutions to systems of equations.

You've probably already got a great understanding of how to solve systems of equations by either subtraction or elimination, so the only thing you might be having trouble with when dealing with this method is the graphs.  Remember that the lines can only cross in one place, and that this method is often inaccurate because you sometimes have to estimate where the lines actually cross.

Example:

```1. Solve:    y = x + 1  and  y = -2x + 4
Solution: Begin by drawing a couple of tables (one for each equation)
and filling them in.

y = x + 1

------------------
| x | 0 | 2 | -3 |
------------------
| y | 1 | 3 | -2 |
------------------

y = -2x + 4

-----------------------
| x | 0 | 2 | -2 |  4 |
-----------------------
| y | 4 | 0 |  8 | -4 |
-----------------------

Now, plot those points and draw a line connecting them.  Once
that has been done, you will see that the lines intersect at
(1,2) (it is fairly obvious on the graph that it is
exactly (1,2)).

The graph: Example Graph
```
Always be on the lookout for tricky situations, such as systems of equations that when graphed are two parallel lines.  Since they're parallel, they will never intersect, and there will be no solution to that problem.