# use cramers rule to solve each linear system help please

• Dec 9th 2010, 04:05 PM
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 (Crying)

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
• Dec 9th 2010, 04:14 PM
pickslides
Quote:

use cramers rule to solve each linear system

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

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

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

Can you see the pattern?

If not look here

Cramer's rule - Wikipedia, the free encyclopedia
• Dec 9th 2010, 04:38 PM
Soroban

I'll do the first one . . .

Quote:

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

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

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

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

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

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

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

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

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

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

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

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