One of my grade 8 students was working on the graphical solution method for simultaneous equations.
4x – 5y = 14
3x + y = 1
He plotted the lines on the graph paper and as expected, lines cut at ( 1, -2 )
He knew that the intersection point is the solution for such problems. So, ( 1, -2 ) was the solution.
Before writing this answer, he paused for a moment and asked ,
“But, why is this intersection point a solution for these 2 equations?”
He was looking flummoxed by this thought, and I love such confusions. I encourage my students to ask many more such questions. These questions lead us to the path of Guided Discovery.
Rather than answering his question directly, I asked him,” Forget about this simultaneous equation problem. Just tell me what does the term ‘solution’ mean to you?”
He was trying to express his understanding of ‘solution’ but he was at loss of words.
As per the Guided Discovery principle, this is a time to connect the concept to real-world.
I presented a real life problem to him.
You want to book a Math session with me. You are available on Mon, Tues & Wed while I am available on Thurs & Friday.
Me : So, how will you solve this situation ? When can we schedule our session ?
Student : In this scenario, we cannot schedule our session. There is no solution!
Me : Let me present a bit different scenario this time.
You want to book a Math session with me. You are available on Mon, Tues & Wed while I am available on Wed, Thurs & Friday.
So, how will you solve this situation ? When can we schedule our session ?
Student : Wednesday works for both of us. We can schedule our session on Wednesday.
Me : Yes, Wednesday solves the purpose for both of us. Good for you & me. Wednesday is the solution in this case.
Let me present one more scenario before we get back to your simultaneous equations and intersection point question. Hopefully, this should give you a complete picture.
You & your best friend want to come together for a Math session this time. You are available on Mon, Tues & Wed; your best friend is available on Tues, Wed & Thurs while I am available on Wed, Thurs & Friday.
So, how will you solve this situation ? When can we schedule our session ?
Student : Wednesday is the only day when all 3 of us are available. We can only schedule our session on Wednesday.
Me : So, I can say that Wednesday is the only solution in this scenario.
Student : Yes!
Me : So, solution is something which satisfies all the given conditions. Right ?
Student : Yes, Wednesday is the only day which suits me, my friend and you too.
Me : Do you see anything related to an ‘Intersection point’ in this solution ?
Student : Yes, I got it! Wednesday is a common point in all 3 calendars, and that’s what ‘Intersection point’ is all about – finding a solution to simultaneous equations.
Me : Perfect!
I would encourage you to discuss this with your children/ students and let me know if it gives them a clearer perspective of intersection point. Your feedback will surely help me in this journey of Making Maths Simple & Visual.
Maths2Art 
Interesting and Intelligent way of making the students understand about the point of intersection.
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I am glad that you found it useful.
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No I feel shameful, by spamming your comment section with appreciation. Again wow.
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Excellent. Another way to explain would be by using roads or railways and using the junctions as an example of intersection…enjoyed reading this!
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Thank you for leaving your kind words here.
Yes, your example is also quite relevant. We need many more such examples to make education more meaningful.
Please do let us know if you would like to write such articles on any topic. We would ne glad to publish it onboard with due credits.
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