For the simultaneous equations ax+by=p and bx-ay=q, show that x=(ap+bq)/(a^2+b^2) and y=(bp-aq)/(a^2+b^2)
I just can't figure out which method to use and how to do it. Because I've never done one without numbers before.
Many thanks in advance.
For the simultaneous equations ax+by=p and bx-ay=q, show that x=(ap+bq)/(a^2+b^2) and y=(bp-aq)/(a^2+b^2)
I just can't figure out which method to use and how to do it. Because I've never done one without numbers before.
Many thanks in advance.
Do it the same way as you would with numbers...
$\displaystyle \displaystyle a\,x + b\,y = p$
$\displaystyle \displaystyle b\,x - a\,y = q$.
Multiply equation 1 by $\displaystyle \displaystyle b$ and multiply equation 2 by $\displaystyle \displaystyle a$ to get
$\displaystyle \displaystyle ab\,x + b^2y = bp$
$\displaystyle \displaystyle ab\,x - a^2y = aq$.
Now subtract equation 2 from equation 1 to eliminate the $\displaystyle \displaystyle x$ term.