# Solving a System of Two Linear Equations Using Cramer's Rule Group the two equations in the following form $ \begin{align} ax+by&=c \\ dx+ey&=f \end{align} $ The solution is then: $ \begin{align} x &= \frac {(b \cdot f) - (c \cdot e)}{(b \cdot d) - (a \cdot e)} \\ y &= \frac {(c \cdot d) - (a \cdot f)} {(b \cdot d) - (a \cdot e)} \end{align} $ Notice that the denominator of both $x$ and $y$ is the same, so when you solve for $x$ you can just copy the denominator. ## Example $ \begin{gather} x + 2y = 11 \\ 2x + y = 10 \\ x = \frac {20 - 11} {4-1} = \frac {9} {3} = 3 \\ y = \frac {22 - 10} 3 = \frac {12} 3 = 4 \end{gather} $