Answer
$x_{1}$ = $\frac{4}{5}$
$x_{2}$ = $\frac{-3}{10}$
Work Step by Step
Cramer's Rule is used to find the solutions to a system of equations.
We first have to turn the system of equations into matrices.
A = $\begin{bmatrix}
3 & -2 \\
-4 & 6
\end{bmatrix}$
We then replace the first column with the column of solutions.
$A_{1}$(b) = $\begin{bmatrix}
3 & -2 \\
-5 & 6
\end{bmatrix}$
We then replace the second column with the column of solutions.
$A_{2}$(b) = $\begin{bmatrix}
3 & 3 \\
-4 & -5
\end{bmatrix}$
We then need to find the determinant of each matrix.
Note: The determinant of a 2x2 matrix is ad-bc where $\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}$
det(A) = (3)(6) - (-2)(-4) = 18 - 8 = 10
det($A_{1}$(b)) = (3)(6) - (-5)(-2) = 18 - 10 = 8
det($A_{2}$(b)) = (3)(-5) - (3)(-4) = -15 + 12 = -3
We then use the formula:
$x_{1}$ = $\frac{det(A_{1}(b))}{det(A)}$ = $\frac{8}{10}$ = $\frac{4}{5}$
$x_{2}$ = $\frac{det(A_{2}(b))}{det(A)}$ = $\frac{-3}{10}$
The solutions to the system are:
$x_{1}$ = $\frac{4}{5}$
$x_{2}$ = $\frac{-3}{10}$