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Calculator to solve three simultaneous linear equations

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To finish one Product A, the process start from machine 1 for 2 minutes then machine 2 for 1 minutes and finally in machine 3 for 2 minutes. For Product B and Product C the time needed are shown in the table below. Compute how many product A , product B, and Product C was produced by reading the total runtime of machine 1, machine 2, and machine 3.



How to write the equations? Focus on the given constraint that need to be satisfied
Constraint number 1: machine 1 will run 2 min for product A then 1 min for product B then 1 minute for product C. Total running time of machine 1 is 180 minutes. First step is to assign variable letter x = number of finished product A ; letter y = number of finished product B , and z = number of finished product C. Writing the constraint number 1 in mathematical expression: 2x + 1y + 1z = 180 minutes machine 1 is running.

Constraint number 2: machine 2 will run 1 min for product A then 3 min for product B, then 2 min for product C. The total running time of machine 2 is 300 minutes. Writing the constraint number 2 in mathematical expression: 1x + 3y + 2z = 300 minutes

Constraint number 3: machine 3 will run 2 min for product A then 1 minute for product B, then 1 min for product C. The total running time of machine 3 is 240 minutes. Writing the constraint number 3 in mathematical expression: 2x + 1y + 1z = 240 minutes



x + y + z = minutes for machine 1 equation 1 or specified constraint number 1 that must be satisfied when you do the final validation if your answer is correct.

x + y + z = minutes for machine 2 equation 2 or specified constraint number 2 that must be satisfied when you do the final validation if your answer is correct.

x + y + z = minutes for machine 3 equation 3 or specified constraint number 3 that must be satisfied when you do the final validation if your answer is correct.



Answer, number of product A, x =
Answer, number of product B, y =
Answer, number of product C, z =

These are solved using Cramer's Rule; Keep in mind that sometimes Cramer's Rule doesn't work. Therefore always substitute the value of x, y, and z to equation 1, 2, and 3 to check if they are valid answer.



Now student and teacher will no longer need to check the test exam paper because it is done automatically. This will save teacher a lot of time in checking paper.

Learning Algebra is very important skill every student must master. Why? Because algebra give student the training and stamina to press on , to formulate, to grapple with complex problem. It trains student to reflect on their thinking during problem solving process, develop the habits of persistent. It trains them to gather proof and evidence for critical analysis.

Today with machine learning and artificial intelligence the hard part of doing actual computation is now easy as you experience from using this software tool. But the concept of Algebra remains the same. Algebra connect the quantitative relationship of physical things like the number of product A, the number of product B, and the number of product C that you want to solve. Algebra deals with representing the physical objects as letter variable like let letter X represent the number of product A, Y represent the number of product B, and letter Z represent the number of product C. Now the teacher job is to help the student to realize that every letter or variable they see in algebraic equation represent a physical object. Trying to convince their student that Algebra is a cool tool because when they are solving algebraic equation they are like playing with physical material in the laboratory but not spending any money for material cost because it is done using paper and pencil or simulation in computer software. Algebra is behind the computer simulation modelling.

When they actually work with actual material things their skills in using Algebra will save them time and money.





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