# Find x and y so each statement about vectors is true

• Mar 30th 2009, 03:55 PM
dancerforlife
Find x and y so each statement about vectors is true
So far, I have gone from the original problem
6<5x-7,5>-8<12,7-3y>= -10<5x+2,6y-1>
to here:
<30x-42,30>-<96,56+24y>=<-50x+20,-60y+10>
<(30x-42)-(96),(30)+ (56+24y)>=<-50x+20,-60y+10>

Am i right? I think the answers are x=59/40 and y=3/7
I have no clue what to do?
• Mar 30th 2009, 10:55 PM
earboth
Quote:

Originally Posted by dancerforlife
So far, I have gone from the original problem
6<5x-7,5>-8<12,7-3y>= -10<5x+2,6y-1>
to here:
<30x-42,30>-<96,56-24y>=<-50x-20,-60y+10> <<<<<<<<<
<(30x-42)-(96),(30)- (56-24y)>=<-50x-20,-60y+10> <<<<<<<<<

Am i right? I think the answers are x=59/40 and y=3/7
I have no clue what to do?

1. I've marked in red (hard to detect, sorry) the wrong signs.

2. Split the 2 vectors into their components:

$\displaystyle \begin{array}{l}30x-42 = -50x-20~\implies~80x = 22~\implies~x = \dfrac{11}{40} \\ 30-(56-24y)=-60y+10~\implies~84y = 36~\implies~y = \dfrac{3}{7}\end{array}$