Answer
The solutions to the system are:
$x_{1}$ = 1
$x_{2}$ = 2
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 = $\begin{bmatrix}
4 & 1 \\
3 & 2
\end{bmatrix}$
We then replace the first column with the column of solutions.
$A_{1}$(b) = $\begin{bmatrix}
6 & 1 \\
7 & 2
\end{bmatrix}$
We then replace the second column with the column of solutions.
$A_{2}$(b) = $\begin{bmatrix}
4 & 6 \\
3 & 7
\end{bmatrix}$
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) = (4)(2) - (1)(3) = 8 - 3 = 5
det($A_{1}$(b)) = (6)(2) - (7)(1) = 12 - 7 = 5
det($A_{2}$(b)) = (7)(4) - (3)(6) = 28 - 18 = 10
We then use the formula:
$x_{1}$ = $\frac{det(A_{1}(b))}{det(A)}$ = $\frac{5}{5}$ = 1
$x_{2}$ = $\frac{det(A_{2}(b))}{det(A)}$ = $\frac{10}{5}$ = 2
The solutions to the system are:
$x_{1}$ = 1
$x_{2}$ = 2
