Question

Consider the system of equations.

Answer 1

Answer: See the attached image below

Solutions are x = -2 and y = 4

I've arranged the tiles into the correct positions, and wrote in the final result for each x and y.

The basic idea is to divide determinants as the vertical bars indicate (they aren't absolute value bars).

In each denominator is the determinant of the matrix $\begin{bmatrix}2 & 1\\-3 & 4\end{bmatrix}$ which are the coefficients of the left hand side of each original equation given to you.

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The numerators are a slight variation of this matrix. The x determinant will have you replace the first column with 0 & 22 getting $\begin{bmatrix}0 & 1\\22 & 4\end{bmatrix}$ which helps figure out the x solution. The y solution is similar as well, but we replace the y column instead of the x column. So that explains the $\begin{bmatrix}2 & 0\\-3 & 22\end{bmatrix}$

After you have the proper determinants set up, you just evaluate each determinant using the formula

$\begin{vmatrix}a & b\\ c & d\end{vmatrix} = a*d - b*c$

and then simplify the results.