On a math test, there were multiple choice and show your work problems. Nanette got 7 multiple choice problems correct and 6 show your-work...

We are given that one student got 7mc and 6 work problems correct for 62 points, and another student got 9mc and 5 work problems correct for 58 total points.

We assume that we want to know the points for correct multiple choice questions and extended response questions.

Let x= points per correct multiple choice question.

Let y= points per correct work problem.

Then we have a system of equations:

7x+6y=629x+5y=58

We are asked...

We are given that one student got 7mc and 6 work problems correct for 62 points, and another student got 9mc and 5 work problems correct for 58 total points.

We assume that we want to know the points for correct multiple choice questions and extended response questions.

Let x= points per correct multiple choice question.

Let y= points per correct work problem.

Then we have a system of equations:

7x+6y=62
9x+5y=58

We are asked to solve the system using matrices.

We can write the system in matrix form as 

`[[7,6],[9,5]]*[[x],[y]]=[[62],[58]]`

There are a number of ways to solve this:

1. Use inverse matrices. If AX=B then A^(-1)AX=A^(-1)B so X=A^(-1)B

The determinant of A is (7*5-9*6)=-19 so the inverse is 

`[[-5/19,6/19],[9/19,-7/19]]` and so

`X=[[x],[y]]=[[-5/19,6/19],[9/19,-7/19]]*[[62],[58]]=[[2],[8]]`

Then each multiple choice question is worth 2 points, and each extended response question is worth 8 points.

2. Use Cramer's rule:

Here `x=|[62,6],[58,5]|/(-19)=-38/-19=2`

`"and" y=|[7,62],[9,58]|/(-19)=-152/-19=8`

We could also put the extended matrix in reduced row-echelon form.

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