Linear Equations for Gold Course Holes

[vorcil]

Gold courses have 18 holes.
each hole has a par, with either 3,4,5
the sum over the holes of one gold course is 78.
the number of par 5 holes is 6 more than the number of par 3 holes

if there are x holes with par 3, y holes with par 4 and z holes with par 5
write down a system of three linear equations linking these quantities

first two are easy
( 1 1 1 18 )
( 3 4 5 78 )
the third one I'm confused how to get to
( 1 0 1 7 ) ?
i solved using row echelon reduction and it doesn't work

the answers say -1 0 1 6
how does it get that?
how am i supposed to know that during a test?
please help

 

[phyzmatix]

Your first two equations look fine to me. For the third, the number of par 5 holes is z the number of par 3 holes is x and the number of par 5 holes is 6 more than the number of par 3 holes so

z = x + 6

or

z - x = 6

Does that help?

 

[vorcil]

Your first two equations look fine to me. For the third, the number of par 5 holes is z the number of par 3 holes is x and the number of par 5 holes is 6 more than the number of par 3 holes so

z = x + 6

or

z - x = 6

Does that help?

Oh, I was having a hard time trying to figure out why it was -x + z
cheers
get it

 

[phyzmatix]

Glad to help