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 

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 

 and so

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

2. Use Cramer's rule:

Here 

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