Question

Explain, in complete sentences, the process of using Cramer’s Rule to solve the following system of equations. Provide the solution to the system.

2x + 7y = 2
3x + 8y = 2

Answer 1

Ok. So first we need to express this system of equations using matrices. For Cramer's rule to be applicable, the variables should be in a column matrix, so we are looking at a matrix equation of the form\[\mathbf{A}\left[\begin{matrix}x \\ y\end{matrix}\right]=\left[\begin{matrix}2 \\ 2\end{matrix}\right] (equation~ 1)\]And we know what A is. So now, we need the determinant of A.\[\det(\mathbf{A})=(2)(8)-(7)(3)=16-21=-5\neq 0\]To solve for x, replace the first column of A with the column matrix on the right-hand side of (1), and then find the determinant. Doing this, we get 2. Simply divide that by our determinant of A, above, to get the solution: x=-2/5. Do the same thing for y, except this time replace the second column of A with the column matrix in (1). Then you get y=2/5.