{[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 "F4 - Syst~00e8mes lin~00e9aires " 2*2 " " - " D~00e9cimaux et fractions " ] [auteurs_aplusix "JF Nicaud " ] [description_aplusix "Exemples : " {and [{dec 5 1}x-{dec 2 7}y=3] [{dec 2 9}x+5y=-4]} " " {and [{frac [2] [3]}x+{frac [5] [6]}y=3] [x+4y=3]} " " ] [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 2 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix " " {for {and [{calculD [ax]}+{calculD [by]}={calculD {frac [10w+v-2] [10]}}] [{calculD [cx]}+{calculD [dy]}={calculD {frac [10(v-3)+w+1] [10]}}]} {and {natAnd 1<=m<=5 2<=n<=4} {natAnd 1<=u<=3 6<=v<=9} [1<=w<=4] [{natAnd {let a=n} {let b={calculD {frac [-10u-v] [10]}}}}] [{natAnd {let c={calculD [1]}} {let d={calculD {frac [10(n+3)+v+3] [10]}}}}] [ad-bc<>0] {number 10}}} " " ] [exercices_aplusix " " {and [4x-{dec 2 6}y={dec 3 4}] [x+{dec 7 9}y={dec 3 4}]} " " {and [3x-{dec 3 8}y={dec 1 6}] [x+{dec 7 1}y={dec 5 2}]} " " {and [4x-{dec 1 7}y={dec 3 5}] [x+8y={dec 4 4}]} " " {and [3x-{dec 3 7}y={dec 3 5}] [x+7y={dec 4 4}]} " " {and [2x-{dec 1 8}y={dec 3 6}] [x+{dec 6 1}y={dec 5 4}]} " " {and [3x-{dec 3 6}y={dec 2 4}] [x+{dec 6 9}y={dec 3 3}]} " " {and [4x-{dec 2 7}y={dec 2 5}] [x+8y={dec 4 3}]} " " {and [2x-{dec 2 6}y={dec 2 4}] [x+{dec 5 9}y={dec 3 3}]} " " {and [3x-{dec 3 8}y={dec 4 6}] [x+{dec 7 1}y={dec 5 5}]} " " {and [2x-{dec 1 7}y={dec 3 5}] [x+6y={dec 4 4}]} " " " " ] [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 2 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix {for {and [{calculD [ax]}+{calculD [by]}={calculD {frac [10w+v-2] [10]}}] [{calculD [cx]}+{calculD [dy]}=w]} {and {natAnd 1<=m<=5 2<=n<=4} {natAnd 1<=u<=3 6<=v<=9} [1<=w<=4] [{natAnd {let a={calculD {frac [10(n+3)+v+3] [10]}}} {let b={calculD {frac [-10u-v] [10]}}}}] [{natAnd {let c={calculD [1]}} {let d=n}}] [ad-bc<>0] {number 10}}} " " ] [exercices_aplusix {and [{dec 7 2}x-{dec 1 9}y={dec 2 7}] [x+3y=2]} " " {and [{dec 7 9}x-{dec 3 6}y={dec 4 4}] [x+4y=4]} " " {and [6x-{dec 3 7}y={dec 2 5}] [x+2y=2]} " " {and [{dec 7 9}x-{dec 1 6}y={dec 3 4}] [x+4y=3]} " " {and [{dec 8 1}x-{dec 1 8}y={dec 1 6}] [x+4y=1]} " " {and [{dec 7 9}x-{dec 1 6}y={dec 4 4}] [x+4y=4]} " " {and [{dec 6 1}x-{dec 3 8}y={dec 1 6}] [x+2y=1]} " " {and [{dec 5 9}x-{dec 1 6}y={dec 1 4}] [x+2y=1]} " " {and [{dec 6 9}x-{dec 2 6}y={dec 3 4}] [x+3y=3]} " " {and [{dec 6 2}x-{dec 3 9}y={dec 2 7}] [x+2y=2]} " " " " ] [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 {for {and [{calculQ [a]}x+{calculQ [b]}y=w-1] [cx+dy=v-3]} {and {natAnd 1<=m<=5 2<=n<=4} {natAnd 2<=u<=5 6<=v<=9} [2<=w<=4] [{hcf (m;n)}=1] [{hcf (u;2n)}=1] [{natAnd {let a={calculQ {frac [m] [n]}}} {let b={calculQ {frac [u] [2n]}}}}] [{natAnd {let c=1} {let d=w}}] [ad-bc<>0] {number 10}}} " " ] [exercices_aplusix " " {and [{frac [3] [4]}x+{frac [3] [8]}y=3] [x+4y=6]} " " {and [{frac [5] [4]}x+{frac [5] [8]}y=1] [x+2y=4]} " " {and [{frac [3] [4]}x+{frac [5] [8]}y=3] [x+4y=5]} " " {and [{frac [2] [3]}x+{frac [5] [6]}y=3] [x+4y=3]} " " {and [{frac [5] [4]}x+{frac [5] [8]}y=3] [x+4y=6]} " " {and [{frac [5] [4]}x+{frac [3] [8]}y=3] [x+4y=5]} " " {and [{frac [2] [3]}x+{frac [5] [6]}y=1] [x+2y=5]} " " {and [{frac [3] [4]}x+{frac [5] [8]}y=2] [x+3y=6]} " " {and [{frac [1] [2]}x+{frac [5] [4]}y=3] [x+4y=3]} " " {and [{frac [1] [3]}x+{frac [5] [6]}y=2] [x+3y=4]} " " " " ] [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 {for {and [{frac [mx+ny] [w]}=w-1] [{frac [ux+vy] [v-1]}=v-2]} {and {natAnd 1<=m<=4 2<=n<=4} {natAnd 2<=u<=5 3<=v<=6} [2<=w<=4] [{natAnd {let a={frac [m] [w]}} {let b={frac [n] [w]}}}] [{natAnd {let c={frac [u] [v-1]}} {let d={frac [v] [v-1]}}}] [ad-bc<>0] {number 10}}} " " ] [exercices_aplusix " " {and [{frac [4x+3y] [4]}=3] [{frac [5x+5y] [4]}=3]} " " {and [{frac [4x+4y] [3]}=2] [{frac [5x+4y] [3]}=2]} " " {and [{frac [2x+3y] [4]}=3] [{frac [4x+5y] [4]}=3]} " " {and [{frac [x+4y] [2]}=1] [{frac [2x+4y] [3]}=2]} " " {and [{frac [x+3y] [3]}=2] [{frac [3x+6y] [5]}=4]} " " {and [{frac [4x+2y] [3]}=2] [{frac [5x+5y] [4]}=3]} " " {and [{frac [4x+2y] [3]}=2] [{frac [3x+5y] [4]}=3]} " " {and [{frac [2x+2y] [4]}=3] [{frac [2x+6y] [5]}=4]} " " {and [{frac [x+2y] [3]}=2] [{frac [2x+5y] [4]}=3]} " " {and [{frac [x+2y] [2]}=1] [{frac [4x+4y] [3]}=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 {for {and [{frac [mx-ny] [w]}={frac [(w-1)x+y-n+1] [u-1]}] [{frac [-ux+vy] [v-1]}={frac [2x+(v-2)y+u-1] [n-1]}]} {and {natAnd 1<=m<=4 2<=n<=4} {natAnd 2<=u<=5 3<=v<=6} [2<=w<=3] [{natAnd {let a={frac [m] [w]}-{frac [w-1] [u-1]}} {let b={frac [-n] [w]}-{frac [1] [u-1]}}}] [{natAnd {let c={frac [-u] [v-1]}-{frac [2] [n-1]}} {let d={frac [v] [v-1]}-{frac [u-1] [n-1]}}}] [ad-bc<>0] {number 10}}} " " ] [exercices_aplusix " " {and [{frac [2x-4y] [3]}={frac [2x+y-3] [3]}] [{frac [-4x+6y] [5]}={frac [2x+4y+3] [3]}]} " " {and [{frac [3x-4y] [3]}=2x+y-3] [{frac [-2x+6y] [5]}={frac [2x+4y+1] [3]}]} " " {and [{frac [4x-3y] [3]}={frac [2x+y-2] [4]}] [{frac [-5x+6y] [5]}={frac [2x+4y+4] [2]}]} " " {and [{frac [2x-4y] [3]}={frac [2x+y-3] [2]}] [{frac [-3x+6y] [5]}={frac [2x+4y+2] [3]}]} " " {and [{frac [3x-3y] [2]}=x+y-2] [{frac [-2x+6y] [5]}={frac [2x+4y+1] [2]}]} " " {and [{frac [4x-3y] [3]}={frac [2x+y-2] [2]}] [{frac [-3x+6y] [5]}={frac [2x+4y+2] [2]}]} " " {and [{frac [x-4y] [3]}={frac [2x+y-3] [3]}] [{frac [-4x+6y] [5]}={frac [2x+4y+3] [3]}]} " " {and [{frac [x-4y] [2]}={frac [x+y-3] [3]}] [{frac [-4x+3y] [2]}={frac [2x+y+3] [3]}]} " " {and [{frac [2x-4y] [3]}=2x+y-3] [{frac [-2x+3y] [2]}={frac [2x+y+1] [3]}]} " " {and [{frac [3x-2y] [2]}={frac [x+y-1] [3]}] [{frac [-4x+4y] [3]}=2x+2y+3]} " " " " ] [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 1 " " ] [exercices_aleatoires oui] [type_exercice operator_solve] [consigne_exercice " " ] [reserve_aplusix " " ] [exercices_aplusix " " " " ] [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 ()]}]}