Indigo Sky High School

A Linear System

Introduction

Indigo Sky High School is a very successful high school with an extremely high university acceptance rate. It is known as a prestigious high school where all grade 12 students get into university. However it wasn't always like this. The old principal has just retired and a new one is hired to run the school. To keep the school to continue to be successful, the new principal gathers statistics from when this school was first established (in 1967) to figure out in what year did the trend of all students get into university first begin. This would help him understand what activities and what curriculum the school must continue using to help the students excel.

Data Table

First, relevant statistics and data must be collected.
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The data shows the two linear relations which can also be written in two separate equations:


1) The total number of grade 12 students in the school.

LET:

x = number of years after the school was established

y = total number of grade 12 students in the school


y = 76x + 150




2) The number of grade 12 students accepted into university.

LET:

x = number of years after the school was established

y = number of grade 12 students accepted into university


y = 90x + 10

Graph

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Point of Intersection

The point of intersection is shown on the graph, however there is also another method to find the solution of this linear system.


1) y = 76x +150

2) y = 90x + 10

Substitute this value of 'y' from equation 1).


76x + 150 = 90x +10

150 - 10 = 90x - 76x

140 = 14x

x = 140/14

x = 10

For the value of 'y' substitute the value of 'x' from equation 1).


y = 76(10) + 150

y = 760 + 150

y = 910



Therefore the point of intersection is (10, 910).


This point represents that after 10 years the school was established (in 1977), there were a total of 910 grade 12 students that were in Indigo Sky High School and a total of 910 grade 12 students that were accepted into university. So, in that year all 12th grade students were accepted into university.

Conclusion

In summary, the first year of when all grade 12 students in Indigo Sky High School were accepted into university was 10 years after the school was established. The year was 1977, with a total 910 grade 12 students at Indigo Sky High School and 910 12th grade students who were accepted into university.


The new principal should reflect back on the teaching methods and activities of 1977 so he can help his high school continue to prosper.