do clW vwly ryKI smIkrx - PowerPoint PPT Presentation

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  1. do clWvwlyryKIsmIkrx klws : nOvIN AiDAwie : pihlw mnpRIqisMG mYQmwstr s.h.sig`l (luiDAwxw)

  2. pUrvigAwx • ie`k Gwq qo kI Bwv hY? • cl qo kI Bwv hY? • ie`k cl qo kI Bwv hY? • kI qusIN do clW vwly ryKI smIkr bwry jwxdy ho? AwE bic`E A`j AsIN do clW vwly ryKI smIkr bwry jwxgyN[

  3. jwx pCwx • smIkrx ie`k AijhI smwnqw nUM ikhw jWdw hY ijs iv`c ie`k jW v`D AigAwq rwSIAW AwaudIAW hox , iehnw rwSIAW nMU cl ikhw jWdw hY [ • jdoN iksy smIkrx iv`c kyvl ie`k hI cl hovy qW ies cl dI Gwq 1 hovy qw Aijhw smIkrx ie`k cl vwlw smIkrx khwauNdw hY[

  4. ie`k cl vwlw smIkrx ies qrHW dw huMdw hY[ • ax+ b + 0,a≠0 • X=− ieh ryKI smIkrx dw h`l hY[ • audwhrx dy qOr qy: • 3x +4=5,2x+5= x+9, • (x-2)²=x²+1; ieh swry smIkrx ie`k cl vwly ryKI smIkrx hn[ b a 3 2

  5. iehnW swrIAW smIKrxw iv`c koeI vI ie`k cl vwlw ryKI smIkrx nhIN hY[ 1 u • x =+2 = x²-1, (x-2) (x+1) = 3.u + = 5

  6. ie`k cl vwly smIkrx dw h`l • cl dw ie`k Aijhw mu`l , ijhVw vwsqivk sMiKAw dy rUp iv`c hovy Aqy ijs nwl smIkrx dy dovyN pwsy brwbr ho jwx,smIkrx dw h`l AKvwauNdw hY[ • audwhrx leI • smIkrx 3x+4 =−5 iv`c • jdoN AsIN x dI QW qy -3 lYNdy hW qW, swnUM pRwpq huMdw hY • K`bw pwsw = 3(-3)+4= -9 +4= -5= s`jw pwsw • ikauNik x=-3 leI K`bw pwsw = s`jw pwsw (-5) hn, • ies leI ‘-3’ smIkrx 3x+4=-5 dw h`l hY[

  7. smIkrx dw h`l pqw krn leI hyT ilKy inXmW dI vrqoN kIqI jWdI hY[ • ie`ko ijhI rwSI nUM dovyN pwsy joVn qy smwnqw nhIN bdldI[ • ie`ko ijhI rwSI nUM dovyN pwsy qoN Gtwaux qy smwnqw nhIN bdldI[ • ie`ko ijhi rwSI (≠ 0 nw isPr) duAwrw dovyN pwisAW nUM guxw krn qy smwnqw nhIN bdldI[ • ie`ko ijhi rwSI (≠ 0 nw isPr) duAwrw dovyN pwisAW nUM Bwg krn qy smwnqw nhIN bdldI[

  8. sQwn pirvrqx • ie`k pwsy qoN ie`k pd AidRSt ho ky dUsr pwsy bdly hoey icMnHW nwl jdoN pRgt hovy qW ies ikirAw nUM sQwn pirvrqx kihMdy hn[ • audwhrx 1: smIkrx 5x +9 = 2x + 21 nUM h`l kro[

  9. sQwn pirvrqx • h```````l: swnUM id`qw hY: • 5x+9= 2x + 21 • 5x+9+(-9)=2x+21+(-9) dovyN pwisAW iv`c -9 joVn qy • 5x=2x+12 • 5x-2x=2x+12-2x [dovyN pwsy 2x Gtwaux qy] • 3x =12 • x=4 [ dovy pwsy 1/3 nwl guxw krn qy] • ies leI, x=4 id`qy gey smIkrx dw h`l hY[

  10. AiBAws

  11. hl kro • X=2,y=5 (2x-3y=-11) • X=2,y=5 (5x+3y=4)

  12. iehnWsmIkrnwnUMgrwPduAwrwsulJwE • X=4 • Y=-3 • X=0 • 3y-15=0 • X-y=0

  13. sRoq: pMjwb skUl is`iKAw borf dI novIN SRyxI dI pwT-pusqk, www.heathersanimations.com www.google.com