Grasple has multiple check methods using the Computer Algebra System (CAS) which can be used within the editor to indicate when the answer of a student should be marked correct/incorrect. A full list of current options can be found in this article.

This article covers the **same Solution to System of Equations as** check. There are four sections in this article:

- When to use the same Solution fo System of Equations as check?
- Example cases
- An example exercise
- How does the same Solution fo System of Equations as check work?

## When to use the same Solution fo System of Equations as check?

Do you have a question where you want students to solve the system of equations where the answer contains free variables? In that case, use this check. You can provide a single solution to the system of equations containing free variables and the check will determine whether the solution provided by the student is describing the same Solution to the System of Equations.

## Example cases

Below you can see example cases on when the "same Solution to System of Equations as" is true and when it will return false.

## An example exercise

The following steps describe in short how to do this.

- Create a new exercise with type "
*Equation*". - Set the check type of the exercise by changing the answer rule relation to "
*same Solution to System of Equations as*". Read more about answer rules here. - Give a correct (minimal) complete solution to the system of equations by. This solution will be used to test whether the answers given by learners are correct.
- Go to preview mode and test different answers.
- (Optional) add more detailed feedback/explanation to the exercise.

## Steps

#### Step 1: create a new exercise with type "Equation"

Build up your exercise as you always do: add a description of the question, add the question itself, provide a correct answer (in the answer box) and (optionally) add more detailed feedback.

See an example below:

#### Step 2: set the check-type to "Solution to system of equations"

Click on the "edit answers and specific feedback" button and change the relation for the main (i.e. first) answer rule to "**same Solution to System of Equations as**".

#### Step 3: give a correct complete solution to check answers with

Give a correct complete (but minimal) solution as the correct answer in the edit view. This solution will be used to check whether the answers given by learners are also correct complete solutions for the system of equations.

To create a solution, use the matrix insert menu to insert vectors.

**Step 4: test different correct and incorrect answers**For our sample exercise a correct answer is a solution particular solution satisfying A*x = b and two linear independent homogeneous vectors which satisfy A*u = 0. Additionally, the free variables are r and s (which is also correct).

And an incorrect answer for our sample exercise is a solution where the two homogeneous vectors are linear dependent.

#### Step 5: add more detailed feedback

Automatic feedback will be shown to student about whether they have the answer correct or incorrect including a correct answer.

However more detailed explanation on when answers are correct help the learners in learning from both their correct as incorrect answers.

You can add general feedback in the green "Detailed solution" box and orange "Question at wrong answer" box. For more **specific feedback** based on the characteristics of the student answer, check out the answer rules options.

## How does the same Solution fo System of Equations as check work?

The method checks whether the given solution and the student answer are both a solution to the same system of equations. This is done in four steps:

- Check if number of free variables are the same
- Check if homogeneous are linear independent
- Check if the homogeneous vectors of the answer are all linear combinations of the given homogeneous solution
- Check if the particular solution in the student answers is a linear combination of the given particular solution and the homogeneous solution vectors

Do you want to know more about this check, whether you should use it for your exercise or any of the other checks? Please let us know via the chat icon in the right bottom of the screen!