Opening your next discovery…
When do two equations supply independent information?
Your discovery goalModel two contextual linear constraints, eliminate a variable and distinguish a unique common solution, no solution and infinitely many solutions.
Mapping checkedA prediction is a starting idea. You can revise it after exploring.
Use at least 40 characters and include an observation. Your writing is saved as evidence; it is not automatically judged for accuracy.
This records completion of this demonstration. It is not an official grade or a claim of mastery.
Author two ticket constraints, build an elimination ledger, substitute a common solution and construct three kinds of line pairs.
Model two contextual linear constraints, eliminate a variable and distinguish a unique common solution, no solution and infinitely many solutions.
State what you changed. Describe the result using an observation from the model. Connect the observation to the idea you are learning, then try a different case to test your explanation.
Build on what you know. Discover where it leads.
Open the learning mapCurrent syllabus body inspected: graphical solutions, consistency, algebraic conditions, elimination/substitution and situational modelling. This lab does not claim complete substitution practice.
Current chapter body inspected for modelling, elimination and solution classification. Original ticket/constraint tasks. Substitution practice and full chapter coverage are not claimed.
Mapping scope: Original classroom ticket case using invented credits. Ticket counts must be non-negative integers, while the transfer classifies real solution sets. Lines may cross outside the finite graph window; exact algebra, not viewport appearance, classifies them. Zero rows are not treated as lines. Broader substitution practice remains a gap.
The explanations, models and assessments on labs.bodhiclasses are original learning activities. An official reference establishes curriculum context; it does not imply approval of this activity by CBSE or NCERT.
Investigation 01 · model, eliminate, verify
An expedition team bought 12 entry tickets. Student tickets cost 2 credits each; guide tickets cost 3 credits each. The total was 31 credits. Let x be the student-ticket count and y the guide-ticket count. Find a pair that satisfies both clues.
Enter your own two equations in ax + by = c form. Whole-number coefficients from −1000 to 1000 are accepted, including negative non-zero scaled versions and swapped clue order. A zero row is rejected. Two convenient starting rows are deliberately not the story’s equations.
Graph window: −2 to 14 on each axis. Its clipping does not decide how many real solutions exist.
Keep the two original constraints. Multiply each by a non-zero whole number, then add or subtract the resulting rows so that exactly one variable disappears. Multipliers from −1000 to 1000 cover every allowed integer coefficient pair.
Investigation 02 · construct the solution types
Keep the first constraint x + y = 6. Change the second equation and retain one correctly classified example of each type: a unique real solution, no real solution, and infinitely many real solutions. The notebook retains checked cases; editing inputs revokes the current proof until you check again.
This part considers real-valued quantities, not ticket counts. Crossing outside the graph window is still a unique algebraic solution.
No checked pairs yet. Construct each relationship rather than recording the same case repeatedly.
A new report states x + y = 6 and 2x + 2y = 15 for the same two quantities. Does any real pair satisfy both exact reports?
Original contextual modelling and elimination mapped to NCERT X chapter 3 and current CBSE X syllabus. Row operations here retain the original pair; replacing both originals by one derived equation would lose information. UI coefficient rows are bounded whole numbers, avoiding ambiguous floating-point proportionality. Graphs are schematic finite windows. Substitution is used for verification; a full substitution-method practice sequence is not claimed.
