{[Aplusix {[modele aplusix_modele] [noms_prop (objet statut_aplusix sorte_activite_aplusix titre_aplusix auteurs_aplusix description_aplusix discipline_aplusix theme_aplusix niveau_aplusix age_aplusix mots_cles_aplusix domaine_calcul domaine_bouton_calcul niv_alg_dyn nombre_maxi_exercices exercices_aleatoires les_langues langage_repertoire lexique_multilingue commentaires_widget nombre_phases_aplusix)] [objet Aplusix] [titre_aplusix "F5 - Syst~00e8mes lin~00e9aires ~00e0 2 inconnues " - " 0, 1 ou une infinit~00e9 de solutions " ] [auteurs_aplusix "JF Nicaud " ] [description_aplusix "Exemples : " {and [3x+2y=5] [9x+6y=15]} " " {and [3x+3y=-4] [4x-3y=2] [2x+9y=-10]} " " ] [discipline_aplusix "Math " ] [theme_aplusix "Syst~00e8mes lin~00e9aires " ] [niveau_aplusix " " ] [age_aplusix " " ] [mots_cles_aplusix " " ] [langue_aplusix " " ] [nombre_phases_aplusix 8] [phases (Aplusix_Phase1 Aplusix_Phase2 Aplusix_Phase3 Aplusix_Phase4 Aplusix_Phase5 Aplusix_Phase6 Aplusix_Phase7 Aplusix_Phase8)] [nombre_maxi_exercices " " ] [exercices_aleatoires oui] [statut_aplusix 2] [domaine_calcul nombres_reels] [domaine_bouton_calcul calculs_7] [niv_alg_dyn 2] [les_langues " " ] [langage_repertoire " " ] [lexique_multilingue " " ] [commentaires_widget " " ] [sorte_activite_aplusix libre]}] [Aplusix_Phase1 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase1] [numero_phase 1] [titre_phase " " ] [explication_phase " " ] [nombre_maxi_exercices 1 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix "infinit~00e9 " {for {and [ax+by=u] [kax+kby=ku]} {and [{natAnd -4<=a<=4 {abs [a]}>=1}] [{natAnd -4<=b<=4 {abs [b]}>=2}] {natAnd -5<=u<=5 u<>0} [3<=k<=4] {number 10}}} " " ] [exercices_aplusix " " {and [-4x-2y=2] [-16x-8y=8]} " " {and [x+4y=-5] [4x+16y=-20]} " " {and [-4x+4y=-2] [-16x+16y=-8]} " " {and [3x+2y=5] [9x+6y=15]} " " {and [-4x+2y=-5] [-16x+8y=-20]} " " {and [3x+2y=3] [12x+8y=12]} " " {and [x+3y=-5] [3x+9y=-15]} " " {and [3x-4y=-1] [12x-16y=-4]} " " {and [4x-4y=-3] [12x-12y=-9]} " " {and [-4x+2y=-3] [-12x+6y=-9]} " " " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase2 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase2] [numero_phase 2] [titre_phase " " ] [explication_phase " " ] [nombre_maxi_exercices 1 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix "infinit~00e9 " {for {and [cax+cby=cu] [kax+kby=ku]} {and [{natAnd -4<=a<=4 {abs [a]}>=1}] [{natAnd -4<=b<=4 {abs [b]}>=2}] {natAnd -5<=u<=5 u<>0} [3<=k<=4] [{natAnd -4<=c<=4 {abs [c]}>1}] [{abs [a]}<>{abs [b]}] [{abs [c]}<>{abs [k]}] {number 10}}} " " ] [exercices_aplusix " " {and [-12x+8y=-4] [9x-6y=3]} " " {and [-16x+12y=-4] [12x-9y=3]} " " {and [8x+6y=6] [-16x-12y=-12]} " " {and [-4x+6y=-8] [6x-9y=12]} " " {and [-6x-8y=10] [-12x-16y=20]} " " {and [12x-8y=-8] [-9x+6y=6]} " " {and [-4x-16y=4] [-3x-12y=3]} " " {and [12x+9y=15] [16x+12y=20]} " " {and [9x-12y=-3] [12x-16y=-4]} " " {and [-6x-4y=2] [-12x-8y=4]} " " " " " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase3 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase3] [numero_phase 3] [titre_phase " " ] [explication_phase " " ] [nombre_maxi_exercices 2 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix 1 " solution " {for {and [ax+by=u] [cx+dy=v] [(2a-c)x+(2b-d)y=2u-v]} {and [{natAnd -4<=a<=4 {abs [a]}>=2}] [3<=b<=4] [3<=c<=4] [{natAnd -4<=d<=4 {abs [d]}>=2}] {natAnd -5<=u<=5 -5<=v<=5} [ad-bc<>0] {natAnd u<>0 v<>0} [{natAnd {abs [a]}<>{abs [c]} {abs [b]}={abs [d]}}] {natAnd 2a-c<>0 2b-d<>0} {number 10}}} " " ] [exercices_aplusix " " {and [4x+3y=-4] [3x-3y=-5] [5x+9y=-3]} " " {and [2x+4y=-5] [3x+4y=-2] [x+4y=-8]} " " {and [-2x+4y=-5] [3x+4y=-4] [-7x+4y=-6]} " " {and [-2x+4y=-5] [3x-4y=-3] [-7x+12y=-7]} " " {and [4x+4y=-3] [3x+4y=-2] [5x+4y=-4]} " " {and [-3x+4y=5] [4x-4y=-2] [-10x+12y=12]} " " {and [-2x+3y=1] [3x+3y=-5] [-7x+3y=7]} " " {and [4x+3y=3] [3x-3y=4] [5x+9y=2]} " " {and [3x+4y=1] [4x+4y=1] [2x+4y=1]} " " {and [3x+3y=3] [4x-3y=-2] [2x+9y=8]} " " " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase4 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase4] [numero_phase 4] [titre_phase " " ] [explication_phase " " ] [nombre_maxi_exercices 2 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix 1 " solution " {for {and [ax+by=u] [cx+dy=v]} {and [{natAnd -4<=a<=4 {abs [a]}>=2}] [3<=b<=4] [3<=c<=4] [{natAnd -4<=d<=4 {abs [d]}>=2}] {natAnd -5<=u<=5 -5<=v<=5} [ad-bc<>0] {natAnd u<>0 v<>0} [{natAnd {abs [a]}<>{abs [c]} {abs [b]}={abs [d]}}] {number 10}}} " " " " ] [exercices_aplusix " " {and [-4x+4y=4] [3x+4y=1]} " " {and [-2x+4y=-4] [4x-4y=-3]} " " {and [2x+4y=-2] [3x-4y=4]} " " {and [4x+3y=-5] [3x-3y=3]} " " {and [2x+3y=1] [3x+3y=3]} " " {and [4x+3y=4] [3x-3y=4]} " " {and [2x+3y=5] [3x-3y=-3]} " " {and [3x+3y=5] [4x-3y=5]} " " {and [-3x+3y=2] [4x+3y=3]} " " {and [-3x+3y=4] [4x-3y=2]} " " " " " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase5 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase5] [numero_phase 5] [titre_phase " " ] [explication_phase " " ] [nombre_maxi_exercices 2 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix 0 " sol " {for {and [cax+cby=cu] [kax+kby=k(u-1)]} {and [{natAnd -4<=a<=4 {abs [a]}>=1}] [{natAnd -4<=b<=4 {abs [b]}>=2}] [{natAnd -5<=u<=5 {abs [u]}>=2}] [3<=k<=4] [{natAnd -4<=c<=4 {abs [c]}>1}] [{abs [a]}<>{abs [b]}] [{abs [c]}<>{abs [k]}] {number 10}}} " " " " ] [exercices_aplusix {and [8x+12y=8] [6x+9y=3]} " " {and [-4x+8y=-10] [-6x+12y=-18]} " " {and [3x-12y=-12] [4x-16y=-20]} " " {and [-3x+9y=9] [4x-12y=-16]} " " {and [-8x-6y=-10] [12x+9y=12]} " " {and [-12x-6y=12] [16x+8y=-20]} " " {and [-3x-6y=-15] [4x+8y=16]} " " {and [-6x+4y=4] [9x-6y=-9]} " " {and [-2x+6y=8] [-4x+12y=12]} " " {and [-8x-16y=8] [6x+12y=-9]} " " " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase6 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase6] [numero_phase 6] [nombre_maxi_exercices 2 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix {for {and [cax+cby=cu] [kax+kby=ku] [max+mby=mu]} {and [{natAnd -4<=a<=4 {abs [a]}>=1}] [{natAnd -4<=b<=4 {abs [b]}>=2}] {natAnd -5<=u<=5 u<>0} [3<=k<=4] [{natAnd -4<=c<=4 {abs [c]}>1}] [2<=m<=4] [{abs [a]}<>{abs [b]}] [{natAnd {abs [c]}<>{abs [k]} {abs [c]}<>{abs [m]} {abs [k]}<>{abs [m]}}] {number 10}}} " " ] [exercices_aplusix {and [-8x+12y=-4] [-6x+9y=-3] [-4x+6y=-2]} " " {and [4x-12y=-12] [-3x+9y=9] [-2x+6y=6]} " " {and [-6x-12y=-15] [8x+16y=20] [4x+8y=10]} " " {and [-3x+6y=15] [-4x+8y=20] [-2x+4y=10]} " " {and [6x+8y=10] [12x+16y=20] [9x+12y=15]} " " {and [-8x-4y=6] [12x+6y=-9] [16x+8y=-12]} " " {and [-4x+8y=8] [6x-12y=-12] [8x-16y=-16]} " " {and [-9x-6y=3] [12x+8y=-4] [6x+4y=-2]} " " {and [4x-8y=4] [-6x+12y=-6] [-8x+16y=-8]} " " {and [9x-12y=3] [12x-16y=4] [6x-8y=2]} " " " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase7 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase7] [numero_phase 7] [nombre_maxi_exercices 1 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix " " ] [exercices_aplusix " " ] [commentaires_phase " " ] [liste_exercices ()]}] [Aplusix_Phase8 {[modele aplusix_phase_modele] [noms_prop (objet numero_phase nombre_maxi_exercices exercices_aleatoires type_exercice consigne_exercice commentaires_phase reserve_aplusix exercices_aplusix)] [objet Aplusix_Phase8] [numero_phase 8] [nombre_maxi_exercices 1 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix " " ] [exercices_aplusix " " " " ] [commentaires_phase " " ] [liste_exercices ()]}]}