\[ \begin{array}{l} 3 x-4 y=-3 \\ 7 x-2 y=5 \end{array} \] Answer Attempt 1 out of 2 Write the three relevant determinants in any order: \( \square \) , \( \square \) , \( \square \) Solution to the system: \( x= \) \( \square \) \( y= \) \( \square \)

The determinants you will need to solve this system of equations through the method of determinants (also known as Cramer's Rule) are: 1. The main determinant formed by the coefficients of \(x\) and \(y\): \[ D = \begin{vmatrix} 3 & -4 \\ 7 & -2 \end{vmatrix} \] 2. The determinant for \(x\) where we replace the first column of coefficients with the constant terms: \[ D_x = \begin{vmatrix} -3 & -4 \\ 5 & -2 \end{vmatrix} \] 3. The determinant for \(y\) where we replace the second column of coefficients with the constant terms: \[ D_y = \begin{vmatrix} 3 & -3 \\ 7 & 5 \end{vmatrix} \] Now, let's find the solution to the system: To solve for \(x\) and \(y\) using Cramer’s Rule: 1. Calculate \(D\), \(D_x\), and \(D_y\). 2. Use the formulas: \(x = \frac{D_x}{D}\) and \(y = \frac{D_y}{D}\). Plugging in those determinants will give you the values for \(x\) and \(y\)! Happy calculating!