Question 359714
First, name your variables.
No holes-in-one. So there are only three variables.
Let {{{B}}} be the number of birdies, {{{P}}} the number of pars, {{{G}}} the number of bogeys.
and each have a score of 2,3, and 4 respectively.
You know that 
She played 18 holes.
1.{{{B+P+G=18}}}
"she has made 4 more pars than birdies and bogeys combined"
{{{P=4+(B+G)}}}
2.{{{-B+P-G=4}}}
"Her total score was 55"
3.{{{2B+3P+4G=55}}}
.
.
.
1.{{{B+P+G=18}}}
2.{{{-B+P-G=4}}}
3.{{{2B+3P+4G=55}}}
.
.
.
[A]={{{(matrix(3,3,1,1,1,-1,1,-1,2,3,4))}}}
[x]={{{(matrix(3,1,B,P,G))}}}
[b]={{{(matrix(3,1,18,4,55))}}}
.
.
.
[A][x]=[b]
[x]=[A]inv[b]
.
.
.
det[A]={{{4}}}
.
.
.
[A]={{{(1/4)*(matrix(3,3,7,1,-2,2,2,0,-5,-1,2))}}}
.
.
.
[x]={{{(matrix(3,1,B,P,G))=(matrix(3,1,3,11,4))}}}
.
.
.
Grace got 3 birdies, 11 pars, and 4 bogeys.