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# Mathematics Paper Presentation Class X

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### Mathematics Paper Presentation Class X

1. 1. Mathematics Paper Presentation Conditions For Consistency for a Given Pair Of Linear Equation
2. 2. What does Linear Equation in Two Variable Consists Of ? <ul><li>ax+by+c=0 </li></ul><ul><li>Where ‘x’ & ‘y’ are the Variables (Whose Values We Don’t Know) </li></ul><ul><li>& </li></ul><ul><li>‘ a’, ‘b’ & ‘c’ are Constants (Any Real Number where a ≠ 0 & b ≠ 0) </li></ul><ul><li>2x+4y+3=0 </li></ul><ul><li>a=2 b=4 c=3 </li></ul>
3. 3. Unique Solution <ul><li>Unique Solution Intersecting Lines </li></ul>
4. 4. Unique Solution <ul><li>2x-y-5=0 --------(i) </li></ul><ul><li>x-y-3=0 --------(ii) </li></ul><ul><li>= = </li></ul>
5. 6. A (3,1) B (2,-1) C (3,0) D (4,1) 1 2 Scale: 1box = 1unit 2x-y-5=0 x-y-3=0 y X' x 0 y’ Table Of Roots For Eq n (i) x 3 2 y 1 -1 Table Of Roots For Eq n (ii) x 3 4 y 0 1
6. 7. Many Solution <ul><li>Many Solutions Coincident Line </li></ul>
7. 8. Many Solution <ul><li>x+y-5=0 ----------(i) </li></ul><ul><li>2x+2y-10=0 -----------(ii) </li></ul><ul><li>= = = </li></ul>
8. 10. A (0,5) B (5,0) C (1,4) D (2,3) Scale: 1box = 1unit x+y-5=0 2x+2y-10=0 y 1 X' 0 x 2 y’ Table Of Roots For Eq n (i) x 0 5 y 5 0 Table Of Roots For Eq n (ii) x 1 2 y 4 3
9. 11. No Solution <ul><li>No Solution Parallel Lines </li></ul>
10. 12. No Solution <ul><li>2x+y-160=0 ---------(i) </li></ul><ul><li>2x+y-150=0 ---------(ii) </li></ul><ul><li>= = = </li></ul>
11. 14. Scale: 1box = 10unit A (50,60) B (40,80) C (50,50) D (30,90) 2x+y-150=0 2x+y-160=0 y 1 X' 0 2 x y’ Table Of Roots For Eq n (ii) x 50 30 y 50 90 Table Of Roots For Eq n (i) x 50 40 y 60 80
12. 15. Unique Solution Many Solution No Solution Consistent Consistent Inconsistent Intersecting Lines Coincident Lines Parallel Lines
13. 16. <ul><li>Thank You </li></ul>