Question

Solve the following using Cramer's Rule:
y = 2x - 13
y = -x + 5

Answer 1

Ok, this is probably the hard way to solve this system, but here we go. First rearrange the given system to a setup friendlier for changing into a matrix. After a little work, we will get\[2x-y=13\]\[x+y=5\]

Answer 2

You with me so far?

Answer 3

Now, we need to change the system into a matrix. The LHS becomes\[A=\left[\begin{matrix}2 &-1\\ 1 & 1\end{matrix}\right]\]

Answer 4

We will substitute the RHS vector (the two numbers right of the equal sign in for the x column and the y column to make A_x and A_y respectively. Those matrices are\[A_x=\left[\begin{matrix}13 & -1\\ 5 & 1\end{matrix}\right]\]\[A_y=\left[\begin{matrix}2 & 13 \\ 1 & 5\end{matrix}\right]\]

Answer 5

Now we apply Cramer's rule. To solve the system we substitute, take some determinants, and get the solution (x,y) for the system.\[x=\frac{detA_x}{detA}=\frac{18}{3}=6\]\[y=\frac{detA_y}{detA}=\frac{-3}{3}=-1\]\[(x,y)=(6,-1)\]

Answer 6

We can check the answer by solving using the elimination method, which gives the identical solution.

Answer 7

Hope you understand this...

Answer 8

Thank you so much!

Answer 9

No sweat.