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?

:
let g and a be the number of goals and assists respectively
:
a)2g+1a=86........eq 1
{{{g=red(a-17)}}}............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(a=40)}}}number of assists
:
{{{highlight(g)=red(a-17)=red(40-17)=highlight(23)}}}number of goals
:
c) the solutions represent the number of assists and goals