Question

Use Cramer's rule to solve the system of equations.
{ 2x+3y=4
x-2y=9

Answer 1

Are you studying matrices / linear algebra?

Answer 2

yes!

Answer 3

Great, so how far have you got until now?

Answer 4

(If you're stuck from the beginning, that's fine too though!)

Answer 5

i understand how to do it, just the last step is where i mess up. I only know how to put them into the matrix sets, and solve those out. but i have no idea where to go from there.

Answer 6

As I remember it, you create a square matrix A (left hand side of the equation) and column (that's vertical) vector b (right side of the equation). To get x, you replace the first column of your square matrix with vector b, whereas for y you replace the second column of your square matrix with vector b instead. In both cases, you then take the determinant of the new matrix you've created, and divide by the determinant of the original square matrix A. Does that make sense?

Answer 7

If so, we can try it with the numbers now?

Answer 8

If that doesn't make sense, we can do it using Draw.

Answer 9

\[\left[\begin{matrix}2 & 3 \\ 1 & -2\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}4 \\ 9\end{matrix}\right)\]

Answer 10

yea i understand,

Answer 11

Thanks iven5880!

Answer 12

I'm still working on it. I'm not goot at using this editor

Answer 13

So the original square matrix is the one that iven5880 has laid out, and whose determinant is 2*-2 -3*1 = -4-3=-7.