Systems of Linear Equations

Systems of equations can be solved by a variety of methods. The simplest are:

Substitution

In the system of equations $x+y = 5$ and $x-y = 3$ , we can solve for one of the variables and then substitute that relation into the other equation. From the second equation, we see that $x = y+3$ , so we can rewrite the first equation as $(y+3) + y = 5$ , thus giving us $2y = 2 \implies y = 1$ . Thus $y = 1$ and $x = 4$ .

Elimination

Using the same pair of equations as above, we could also combine the two equations together in such a way as to eliminate one of the variables. In this case, we can simply add them together. Thus we have $(x+y) + (x-y) = 3 + 5$ , which gives us $2x = 8 \implies x = 4$ . Thus $y = 1$ and $x = 4$ .

Easy Math Editor

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`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$