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Students at Green High School and students at Belle High School planned separate field trips to Washington, D.C. Green High School filled three buses (x) and one van (y) with 118 students. Belle High School filled four buses and two vans with 164 students.

The situation above is represented by the following system of equations:

3x + y = 118
4x + 2y = 164
The solution is (36,10)

Explain what the system of equations and the solution both represent.

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Step-by-step explanation:

The system of equations for eq 1 which is 3x + y = 118 represents the Green High School which filled three buses(with a specific number of students identified as x) and a van(with a specific number of students identified as y) with a total of 118 students.

for eq 2; 4x + 2y = 164; represents Belle High School which filled four buses(with a specific number of students identified as x) and two vans(with a specific number of students identified as y) with a total of 164 students.

The solution represents the specific number of students in the buses and vans in eq1 and eq 2 with x being 36 students and y being 10 students.

substituting 36 for x and 10 for y in eq 1;

3(36) + 10 = 108 + 10 = 118 total students for Green High School

substituting 36 for x and 10 for y in eq2;

4(36) + 2(10) = 144 + 20 = 164 total students for Belle High school

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