# Math Help - cramers

1. ## cramers

use cramers rule to solve for x' and y' in terms of x and y
x = 3/5x'-4/5y'
y=4/5x'+3/5y'

i used cramers rule and deduce that x'=7/5 and y'=-1/5
but how do i write my answers in terms of x and y?

2. Originally Posted by alexandrabel90
use cramers rule to solve for x' and y' in terms of x and y
x = 3/5x'-4/5y'
y=4/5x'+3/5y'

i used cramers rule and deduce that x'=7/5 and y'=-1/5
but how do i write my answers in terms of x and y?
1. For convenience transform the system of equations to:

$\left|\begin{array}{rcl}5x&=&3x'-4y' \\ 5y&=&4x'+3y' \end{array}\right.$

2. Then $D=\left|\begin{array}{cc}3&-4\\4&3\end{array} \right| = 25$
and
$D_{x'}=\left|\begin{array}{cc}5x&-4\\5y&3\end{array} \right| = 15x+20y$

3. Thus $x'=\frac{D_{x'}}{D} = \frac{15x+20y}{25} = \frac35x+\frac45y$

4. Determine y'.