Two lines: one solution, no solution, infinitely many solutionsदो रेखाएँ: एक हल, कोई हल नहीं, अनंत हलDo lines: ek solution, koi solution nahi, infinite solutions
NCERT 4.6 · Class 12 Maths · Chapter 4 · interactive diagram
Parts and what they mean
- Axes of each small graph (हर छोटे ग्राफ़ के अक्ष) — Each panel is its own x-y graph.
- Line 2x + 5y = 1 (रेखा 2x + 5y = 1) — First equation of Example 16.
- Line 3x + 2y = 7 (रेखा 3x + 2y = 7) — Second equation of Example 16; it cuts the first line.
- Meeting point (3, −1) (मिलन बिंदु (3, −1)) — The unique solution x = 3, y = −1: consistent.
- Case: unique solution (स्थिति: अद्वितीय हल) — |A| = |2 5; 3 2| = 4 − 15 = −11 ≠ 0, so X = A^{-1}B.
- Line x + 3y = 5 (रेखा x + 3y = 5) — Exercise 4.5, Q3 (first equation).
- Line 2x + 6y = 8 (रेखा 2x + 6y = 8) — Same as x + 3y = 4: parallel to x + 3y = 5, never meets it.
- Case: no solution (inconsistent) (स्थिति: कोई हल नहीं (असंगत)) — |A| = 0 and (\text{adj}\,A)B = \begin{bmatrix} 6 \\ -2 \end{bmatrix} \ne O.
- Line x + y = 2 (रेखा x + y = 2) — An example pair: x + y = 2 and 2x + 2y = 4.
- Line 2x + 2y = 4 (same line) (रेखा 2x + 2y = 4 (वही रेखा)) — Dividing by 2 gives x + y = 2: the two lines lie on top of each other.
- Case: infinitely many solutions (स्थिति: अनंत हल) — |A| = 0 and (\text{adj}\,A)B = O; every point of the line is a solution (consistent).
Original diagram drawn by Simple Learning Hub, based on NCERT 4.6. Report a mistake