Question

How do you solve the system of equations with Cramer's rule?

Answer 1

For a system of equations of the form:

`\begin{gathered} \begin{cases}ax+by=e{} \\ cx+dy=f{}\end{cases} \\ x=\frac{\begin{bmatrix}{e} & {b} \\ {f} & {d}\end{bmatrix}}{\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}} \\ \\ y=\frac{\begin{bmatrix}{a} & {e} \\ {c} & {f}\end{bmatrix}}{\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}} \end{gathered}`

Therefore:

`\begin{gathered} For: \\ 2x+y=0 \\ -3x+4y=22 \end{gathered}`
`x=\frac{\begin{bmatrix}{0} & {1} \\ {22} & {4}\end{bmatrix}}{\begin{bmatrix}{2} & {1} \\ {-3} & {4}\end{bmatrix}}=(0-22)/(8+3)=-2`
`y=\frac{\begin{bmatrix}{2} & {0} \\ {-3} & {22}\end{bmatrix}}{\begin{bmatrix}{2} & {1} \\ {-3} & {4}\end{bmatrix}}=(44-0)/(8+3)=4`