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Linear Systems With Two Variables (SOLVING EQUATION BY GRAPHICAL METHOD)

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Published in: Mathematics
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SOLVING LINEAR EQUATIONS BY GRAPHICAL METHOD

Nihar H / Ahmedabad

11 years of teaching experience

Qualification: B.Com (VNSGU - 2010)

Teaches: Chemistry, English, Mathematics, Physics, Zoology

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  1. NIHAR HIRANI = 7 & 3x ÷ 3 = 7 ) = 2 February 05 , 2016 t x = 0 x = 0 I x ? y = 7 t k x = 1 X 3x ? 3 = 21 3 (x ? y ? ak x Y Y' X 2 5 0 7 The solution setofthe pairof ar q ? 1 on May 24-17 : 52 1 6 X' 1
  2. ? ? 9 ? ? ? (Z'E) s ? 7 a ? ? a ? ? JO ? 40 ? ? ? J *as ? 0 # ? ? s 0000000000000g00000 000000000 ? ? 000 ? 00000 0000000000 000000000 0000000000 000 ? 00000 000000000 ? 000 ? 00000 000000000 ? ? 000 ? 00000 0000000000 ? 000000000 000000000 ? ? 000000000 000000000 ? 000 ? 00000 ? ? ? ? ? 0 ? 0 ? ? 0 000 0000000000 000000000 0000000000 ? 000 ? 00000 000000000 ? 000 ? 00000 0000000000 ? 000000000 0000000000 ? 000000000 000000000 ? ? 000 ? 00000 0000000000 000 ? 00000 0000000000 ? 000000000 000000 ? 000 00 ? 000000 0000000000 000 ? 00000 E ? ? T [ -5 T - ? T € = % 0 ? ? ? 7 8 ? 9 ? 00 02 03 ? ? - 8 = ? 9 = ? ? ? 9 ? = {9 ? % 9 = ? ? ? 9 ? 0 ? ' 90 V ? ? UVHIN
  3. 9 9 ? e 01? ? a JO ? JOJ was umn.los ou S! 0 ? to Z—Z —XE—Z (O)E-Z 0 =XDU!)IDÆ XE ? Z = Z = RE ? XE 0 = x ? D 9 0 ' 90 INVUIH UVHIN
  4. NIHAR HIRANI February 05 , 2016 2 ? ? 3 ) = 5 & ? ? ) , = 2 2 ? ? 3 = 5 ? 3 = 5 - 2x 5-2 % T ? 0 ? = 1 T ? 0 x = 4 ? -2 ? ? -2 : 5-2 ( 1 ) ? -2 ( 4 ) % ? ? = 2 = 2 ? ? Ta ? = 2 T ? ? 0 x = 1 = 2 ? ? ? = 2 ? x ? = 2 ? 2 000000000 ? 0000000000 000000000 0000000000 000000000 0000000000 000000000 ? 0000000000 000000000 ? 0000000000 000000000 ? 0000000000 000000000 0000000000 000000000 ? 0000000000 000000000 ? 0000000000 000000000 ? 0000000000 ? ? 0000 ? 00 ? 0 ? 0 ? 000000 000000000 0000000000 000000000 ? 0000000000 00000g0000000000000 The s ? ? 0 ? set for the pair 0 ? ? e ' eq ? ? t ? ( 1.1 ) May 24-19 : 24 0
  5. 9 9t0 0 ~ en ? q ? autDS satqD4 1 oq autDS am ~ 09 ? ? 0 ? , ba 2 D T 0 ? D ? b ? 00 ? ? 0 ? ? 0 ? ? ? 0 ? ? ? ? ? 00 ? 00 ? ? 0 ? ? 0 ? ? ? 0 ? ? ? ? ? 00 X ? 000 ? 0 ? ? 0 ? ? ? 0 ? ? ? ? ? 00 09 ? 6b ? ? 81 ? KE ? 9 9 ? (K ? ? ) 9 L 81 ? Kg ? 9 9 ? ? I ? ? ? ? D ? X INVUIH UVHIN
  6. NIHAR HIRANI February 05 , 2016 x ? 7y ? 42 & x ? 3y = 6 x ? 7y = ? 42 —7y = ? 42 ? x Taking x = 7 Taking x = 0 -42 -7 -4 2 -0 -4 9 -42 x - 3)' = 6 —3y=6—x Ta x = 0 ak x = 3 The soll set 0 ? pair 0 ? e r equation is ( May 25-11 : 16
  7. 90 : -9 ? e (S'Z) S! uo 7 a , a JO d , , ? ? 0 ? 0 Z 0 T Z OT -0 0 K S Z Z X Z Z XE—OZ XS— 0 Z XE—OZ XS—OZ=KÜ+ 0 = ? 9 ? ' ? / 1 K 9 ? 0 ? X ? = x DULYDJ L = ? x OZ = ? XS = ? x 9 0 ' 90 INVUIH UVHIN
  8. NIHAR HIRANI February 05 , 2016 3x ? 6y = 3900 & x ? 3y = 1300 3x ? 6y = 3900 3 (x +2y= 1300 ) x ? 2 = 1300 +2y= 1300 - x 1300- : 2 a x = 1100 k x = 1300 x 1300 1100 1300-0 1300- : 2 2 0 100 Y 1300-1100 1300- 1300 2 2 200 2 0 2 ? y = 100 ? y = 0 x+3y= 1300 +3y= 1300 - x 1300- : 3 ? ak x = 100 ak x = 1300 1300- 1300- x 1300 100 3 3 1300-100 400 0 Y 3 1300-1300 3 1200 3 0 - 3 0 y= 400 Y X Y' The soll ? " set for pair ? linear equation ( 130 0 ) May 25-11 : 57 8
  9. 6 6 ? -9 ? e uouzmba JO vüDd O ou Sl a a , ? ? 9T ET—6T E -6 ? K ? (s)E -6 T (1)E—61 S T X NE—ST S = x ? XE—6T 6 ? = ? Z ? 9 ? 9 0 9 (Z)E-9 Z = XE ? 9 = 9 = ? XE 6T = ? XE 9 = ? XE 9 0 ' 90 INVUIH UVHIN
  10. NIHAR HIRANI February 05 , 2016 ? + 2 ) ( ? ? 1 ) = ? ? 1 ) ( ? + 1 ) = t ? ? x = 2 t ? ? [ ? x = 0 2 ? 2 ? ? ? ? ? 0 1 ? ? ? x ? 2 ? ? 2 = xy 2 2 2 ? 0 xy ? xy ? x ? 2 ? ? 2 = 0 2 2 ? ? 2 ? ? 2 = 0 ? ? ? 2 ? = 2 2 = 2 ? ? 2 2 ? 2 2 t ? ? 0 x ? t ? ? ? 4 x = 1 ? ? 1 ) ( ? + 1 ) = xy ? ? ? ? ? 1 = xy ? ? ? ? x ? ? - 1 = 0 ? ? ? ? 1 = 0 1 X ? = ? 1 ? ? 0 ? Y 000000000 0000000000 ? ? 0 ? 0000 ? ? ? 00000000 000000000 0000000000 000000000 ? 0000000000 000000000 ? 0000000000 ? 00 ? 0000 ? ? 000000000 000000000 0000000000 ? ? 0 ? 0000 ? ? ? ? ? ? 000000 000000000 0000000000 ? 00 ? ? 000 ? ? ? 0 ? 0 ? 0 ? 00 000000000 ? 0000000000 ? 00 ? 0000 ? ? ? 000000000 000000000 ? 0000000000 ? ? 0 ? 00 ? ? ? ? ? ? ? 0 ? 0 ? 00 000000000 ? 0000000000 X The s ? ? 0 ? se ? for ? ? e p ? of ? 2 ? ? eq ? ? ? 0 ? ? ( 4.3 ) May 25-18 : 28
  11. NIHAR HIRANI February 05, 2016 Draw the graph of the linear equation 3x + Zy = 5 and 3 y = —1 Determine the co-ordinates of the vertices of the triangle formed by these linear equation and x axis. 3x+ 2y=5 2y 5-3x 5-3x -3 2x — 3y -1-2x -1-8 aking x — 1 5—3x taking x taking x -1-2x 1 -1-2x -1-2 (1) -1-2 5—3x 5-3 (3) taking x -1-2(4) Thus the ordinates oftlr veitices ofthe trian•zle by these linear May 24-20:22
  12. NIHAR HIRANI February 05 , 2016 Drawthegraph ofthelinearequationx+y = 10 and x— = 4 Determinethe CO-ordinates Ofthe verticesofthetriangle formed bythese linearequation and xaxis. x ? y = 10 y = 10 ? x t k x = 6 ? a , x = 5 X 0 0 ? 10 - x Y y = 10 - 5 ak x = ? k x ? 4 ? x Y ? 4 ? x X Y Y' Thusthe co ordinatesofthe venices ofthe triangle formed by these linear equation and the ? axis are ( 4 ? 0 ) ( 10 , 0 ) ( 7 , 4 ) May 25-13 : 53
  13. NIHAR HIRANI Draw the graph of the linear equation x + 3y — 6 and 3x 3y — 12 Determine the co-ordinates of the vertices of the triangle formed by these linear equation and y axis. —3 —o 12-2x 3y taking x y 2x 3y 3 3 3 6 3 2 — 12 12 2x 3 taking x taking x y y 3 3 3 3 x taking x o 2 3 1 3 12-2(0) 3 12 0 -3 12 3 4 3 12-2x —3 12 2(3) 3 12-6 -3 6 -3 -2 x Thus the co ordinates of the vertices of the triangle formed by these linear equation and the X axis are (6.0) (0, —4) (012) May 25-19:50 February 05, 2016 13
  14. NIHAR HIRANI February 05, 6 students of class X took part in a quiz. If number of girls is 2 less than the nu mber of boys, find the number of gi rls and boys who took —5 10—5 —2 2016 partin the quiz. Let the number of boys x Number of girls y Total Number of students are 10 x = 10 (1) number of girls is 4 more than the number of boys Boys Boys Girls 4 OR Girls 4 y taking x 10 10 10 3 —4 4 (1) x y y y •.y_4+X taking x — 1 5 taking x y y 7 y taking x 10 5 (2) 6 (2) x x 7 3 1 5 5 5 2 6 x Numbe of boys participants is 3 and number of girls participants is 7 May 26-13:19 14
  15. NIHAR HIRANI 15 students of class X took part in the exa mination of the Indian mathematic Olympiad. The nu mber of boy pa rtici pants is flue less than the number of girls pa rtici pa ntsfind the number of gi rls and boy who participated, Let the number of boys x Number of girls Total Number of students are 15 x + = 15 (1) The number of boy participants is flue less than the number of girls participants Boys Girls OR Boys Girls 5 15 15 y taking x 7 15 y — 15 y 8 Y —5 —5 taking x — 1 7 taking x — 15 y — 15 Y 10 y taking x 7 (2) (2) (1) 5 (2) x Y x Y 7 8 1 6 5 10 2 7 x Numbe of boys participants is 5 and number of girls participants is 10 May 26-11:14 February 05, 2016 15
  16. NIHAR HIRANI February 05, 2016 su en so cass oo pa In a quiz. num ero gir s IS more than the number of boys, find the number of girls and boys who took part in the quiz. Let the number of boys x Number of girls Total Number of students are 10 . x + y 10 (1) number of gi rls is 4 more than the number of boys y taking x y y Boys Boys 10 10 7 — 10 = 10—7 4 4 Girls 4 OR Girls (2) 4 10 y —10-5 (1) x taking x — 5 y x x x (2) taking x taking x x Y x 7 3 1 5 5 2 —2 6 —5 Numbe of boys participants is 3 and number of girls participants is 7 May 26-12:48 16
  17. NIHAR HIRANI February 05 , 2016 ExaminegraphicallywhetherthepairofEquation 5 2x ? 3 ? = 5 & x ? is consistent? Show it on graph 6 2 2 % ? 3 ? = 5 ? t ? ? ? x = 1 2 ? 3 ? = 5 ? ? ? ? gx = 4 5 x = 1 ? = 4 ? 6 2 3 ? = 5 ? 2 ? 5-2 ? 5-2 ? 5 3 5-2 ? 3 1 6 2 3 5-2 ? 1 ) 3 5 x3 x x 6 9y XI 3 ? 1 x 6 6 x 1 2 x3 3 3 6x ? 9 = 15 -34 ) 3 3 ( 2 % ? 3 = 5 ) Eq 1 & 2 ? S07 ? e SO ? is consistent 0 ? d as [ ? ? e & 0 ? ? 0 ? s 1 4 ? 1 Y ? 0000000 ? 0000000000 X May 26-22 : 35

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