SOLUTION: Method of Substitution 8. Ugo plays hockey and is awarded 2 points for each goal and 1 point for each assist. Last season he had a total of 86 points. He scored 17 fewer goals tha

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Question 181727: Method of Substitution
8. Ugo plays hockey and is awarded 2 points for each goal and 1 point for each assist. Last season he had a total of 86 points. He scored 17 fewer goals than assists.
a) Write a linear system to represent the information.
b) Solve the system using the method of substitution.
c) What does the solution represent in the context of this equation?
Please and thank you very much.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
Method of Substitution
8. Ugo plays hockey and is awarded 2 points for each goal and 1 point for each assist. Last season he had a total of 86 points. He scored 17 fewer goals than assists.
a) Write a linear system to represent the information.
b) Solve the system using the method of substitution.
c) What does the solution represent in the context of this equation?
:
let g and a be the number of goals and assists respectively
:
a)2g+1a=86........eq 1
g=red%28a-17%29............eq 2
:
b)take g's value from eq 2 and substitute into eq 1
:
2(a-17)+a=86
:
2a-34+a=86
:
3a=120
:
highlight%28a=40%29number of assists
:
highlight%28g%29=red%28a-17%29=red%2840-17%29=highlight%2823%29number of goals
:
c) the solutions represent the number of assists and goals