# Math Help - use cramers rule to solve each linear system help please

1. ## use cramers rule to solve each linear system help please

use cramers rule to solve each linear system

could somone show me how to do these 5 problems or if u could just show me a few it would be great i got a test tommorow and im clueless so fast help would be appreciated

x-y=7
4x+5y=46

-10x+3y=18
3x-4y=-24

9x+2y=12
5x-3y=19

2x+y=24
-x+6y=14

4x-y=1
7x+8y=-47

2. Originally Posted by shadower4
use cramers rule to solve each linear system

x-y=7
4x+5y=46

$x\displaystyle = \left|
\begin{array}{ c c }
7 & -1 \\
46 & 5
\end{array} \right|
\div \left|
\begin{array}{ c c }
1 & -1 \\
4 & 5
\end{array} \right|$

$y\displaystyle = \left|
\begin{array}{ c c }
1 & 7 \\
4 & 46
\end{array} \right|
\div \left|
\begin{array}{ c c }
1 & -1 \\
4 & 5
\end{array} \right|$

Can you see the pattern?

If not look here

Cramer's rule - Wikipedia, the free encyclopedia

I'll do the first one . . .

$\text{Use Cramer's Rule to solve each linear system.}$

. . $\begin{array}{ccc}x-y &=& 7 \\ 4x+5y&=&46 \end{array}$

. . . . . . . . . . . . .
$x$-coefficients . $y$-coefficients
. . . . . . . . . . . . . . . . . . . $\downarrow \quad\, \downarrow$
We have these numbers: . $\begin{array}{|cc|c|}
1 & \text{-}1 & 7 \\ 4 & 5 & 46 \end{array}$

. . . . . . . . . . . . . . . . . . . . . . . . . $\uparrow$
. . . . . . . . . . . . . . . . . . . . . . .
constants

[1] Find $\,D$, the determinant of the coefficients:

. . $\begin{array}{|cc|} 1 & \text{-}1 \\ 4 & 5\end{array} \;=\;(1)(5) - (\text{-}1)(4) \:=\:5 + 4 \;=\;9$

[2] Find $\,D_x$, the determinant with the $\,x$-coefficients replaced by the constants.

. . $D_x \;=\;\begin{vmatrix}7 & \text{-}1 \\ 46 & 5 \end{vmatrix} \;=\;(7)(5) - (\text{-}1)(46) \;=\;35 + 46 \;=\;81$

. . $\text{Divide by }D\!:\;\;x \;=\;\dfrac{81}{9} \;=\;9$

[3] Find $\,D_y$, the determinant with the $\,y$-coefficients replaced by the constants.

. . $D_x \;=\;\begin{vmatrix}1 & 7 \\ 4 & 46 \end{vmatrix} \;=\;(1)(46) - (7)(4) \;=\;46 - 28 \;=\;18$

. . $\text{Divide by }D\!:\;\;y \;=\;\dfrac{18}{9} \;=\;2$

Therefore: . $\begin{Bmatrix}x &=& 9 \\ y &=& 2\end{Bmatrix}$