Question

Use Cramer's Rule to find solution set:
4x-y=2
3x+2y=7

Answer 1

do you know how to find the determinant of a matrix?

Answer 2

@mathsux4real please engage those who are trying to help you

Answer 3

Left the computer. My fault. And no I do not.

Answer 4

a determinant of a 2x2 matrix is given by\[\left|\begin{matrix}a&b\\c&d\end{matrix}\right|=ad-cb\]

Answer 5

let
\[b= \left(\begin{matrix}2 \\ 7\end{matrix}\right)\]
\[A=\left[\begin{matrix}4 & -1 \\ 3 & 2\end{matrix}\right]\]
then by cramer's rule:
\[x=\det A_1/detA \] \[y=detA_2/detA\]
where A_i is the matrix obtained by replacing the ith column of A with b. first let's find detA_1,detA_2, and det A
\[detA=\det \left[\begin{matrix}4 & -1 \\ 3 & 2\end{matrix}\right]=(4)(2)-(-1)(3)=8+3=11\]
\[detA_1=\det \left[\begin{matrix}2 & -1 \\ 7 & 2\end{matrix}\right]=(2)(2)-(-1)(7)=11\]
\[detA_2=\det \left[\begin{matrix}4 & 2 \\ 3 & 7\end{matrix}\right]=(4)(7)-(3)(2)=22\]
x=detA_1/detA=11/11=1
y=detA_2/detA=22/11=2
x=1 y=2

Answer 6

Wow anonymoustwo44, thank you so much! I really appreciate the thorough explanation. Really helps

Answer 7

yw!

Answer 8

It sucks that you can't give a medal to more than one person :/