# how do you solve simultaneous equations using matrices?

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To solve simultaneous equations using matrices we can use Cramer's Rule.

Let us consider a set of two simultaneous equations.

ax + by = e and cx + dy = f

In matrix notation the equations are written as:

`|~` a b `~|` `|~`x`~|` = `|~` e `~|`

`|__` c d `__|` `|__`y`__|` `|__` f `__|`

x = det [b e , f d] / det[a b , c d]

y = det [a e , c f] / det[a b , c d]

The method can be extended to be used for systems of equations with a larger number of variables also.

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