Question

can someone please help me with Cramer's rule for two-variable systems? Here are the two equations:
3x-2y=7
2x+7y=38

Answer 1

3 -2
2 7

get the determinant, this will be |A|

then replace the 7 into 3 so it will be 7 -2
38 2 38 7. This will be |Ax|.
x = |Ax|/|A|

do this for y

Answer 2

\(\large {\begin{bmatrix}
3&-2&|&\color{red}{7}\\
2&7&|&\color{red}{38}
\end{bmatrix}\\ \quad \\
D=\begin{bmatrix}
3&-2\\
2&7
\end{bmatrix}\qquad
D_x =
\begin{bmatrix}
\color{red}{7}&-2\\
\color{red}{38}&7
\end{bmatrix}\qquad
D_y=
\begin{bmatrix}
3&\color{red}{7}\\
2&\color{red}{38}
\end{bmatrix}\\ \quad \\
x = \cfrac{\textit{determinant of }\begin{bmatrix}
\color{red}{7}&-2\\
\color{red}{38}&7
\end{bmatrix}}{\textit{determinant of }D}\qquad
y = \cfrac{\textit{determinant of }\begin{bmatrix}
3&\color{red}{7}\\
2&\color{red}{38}
\end{bmatrix}}{\textit{determinant of }D}}\)