Answer
The solutions to the system are:
$x_{1}$ = $\frac{5}{6}$
$x_{2}$ = $\frac{-1}{6}$
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 = $\begin{bmatrix}
5 & 7 \\
2 & 4
\end{bmatrix}$
We then replace the first column with the column of solutions.
$A_{1}$(b) = $\begin{bmatrix}
3 & 7 \\
1 & 4
\end{bmatrix}$
We then replace the second column with the column of solutions.
$A_{2}$(b) = $\begin{bmatrix}
5 & 3 \\
2 & 1
\end{bmatrix}$
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) = (5)(4) - (7)(2) = 20 - 14 = 6
det($A_{1}$(b)) = (3)(4) - (7)(1) = 12 - 7 = 5
det($A_{2}$(b)) = (5)(1) - (3)(2) = 5 - 6 = -1
We then use the formula:
$x_{1}$ = $\frac{det(A_{1}(b))}{det(A)}$ = $\frac{5}{6}$
$x_{2}$ = $\frac{det(A_{2}(b))}{det(A)}$ = $\frac{-1}{6}$
The solutions to the system are:
$x_{1}$ = $\frac{5}{6}$
$x_{2}$ = $\frac{-1}{6}$
