Graphing a systems of linear equations?

Question

I'm trying to understand how to graph systems of linear equations.

Say for example we have the following:

$x_1 - 2x_2 = -1$

$-x_1 + 3x_2 = 3$

I'm only used to graphing $x$ and $y$ coordinates, how am I supposed to interpret these?

Thanks in advance!

Answer 1

Hint.

The first equation can be written as $$ x_2=\frac{1}2(x_1+1) $$ and the second one: $$ x_2=\frac13 x_1+1 $$

If you replace $x_1$ and $x_2$ with $x$ and $y$ respectively, you will see something you are familiar with.

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Answer 2

You could

• Treat $x_2$ as $y$
• and $x_1$ as $x$
• so you are drawing
  • $x_2=\frac12x_1+\frac12$
  • $x_2=\frac13x_1+1$
• and label the axes appropriately

Answer 3

Just set $x=x_1, y=x_2$, or when drawing the graph, label the axes $x_1$ and $x_2$ instead of $x$ and $y$. A solution is where the lines cross.