Quiz — 6589c2511c5bc_Enoncé-Série N°1-Systèmes d_équations linéaires.pdf

Question 1 sur 10 20:00

[{"id":42345,"question":"Quelle est la solution du système suivant ? { x + y = 5 ; x - y = 1 }","option_a":"A. (3, 2)","option_b":"B. (2, 3)","option_c":"C. (1, 4)","option_d":"D. (4, 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations, on obtient 2x = 6 ⇒ x = 3. En remplaçant dans la première équation, y = 2. La solution est donc (3, 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. (3, 2)\", \"b\": \"B. (2, 3)\", \"c\": \"C. (1, 4)\", \"d\": \"D. (4, 1)\"}","_debug_options_count":4},{"id":42346,"question":"La méthode de substitution consiste à exprimer une inconnue en fonction de l'autre.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La méthode de substitution consiste effectivement à exprimer une inconnue en fonction de l'autre, puis à substituer cette expression dans la deuxième équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":42347,"question":"Quel système a pour solution (2, -1) ?","option_a":"A. { 2x + y = 3 ; x - 2y = 4 }","option_b":"B. { x + y = 1 ; 2x - y = 5 }","option_c":"C. { 3x - y = 7 ; x + 2y = 0 }","option_d":"D. { x - y = 3 ; 2x + y = 3 }","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant x = 2 et y = -1 dans le système B : 2 + (-1) = 1 et 2*2 - (-1) = 5. Les deux équations sont satisfaites.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. { 2x + y = 3 ; x - 2y = 4 }\", \"b\": \"B. { x + y = 1 ; 2x - y = ","_debug_options_count":4},{"id":42348,"question":"L'interprétation graphique d'un système incompatible montre deux droites parallèles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un système incompatible n'a pas de solution, ce qui se traduit graphiquement par deux droites parallèles (même coefficient directeur).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":42349,"question":"Quelle est la solution du système ? { 3x + 2y = 7 ; x - y = 1 }","option_a":"A. (1, 0)","option_b":"B. (3, 2)","option_c":"C. (2, 1)","option_d":"D. (1, 2)","option_e":"","option_f":"","bonne_reponse":"c","explication":"En utilisant la méthode de substitution (x = y + 1), on obtient 3(y+1) + 2y = 7 ⇒ 5y = 4 ⇒ y = 0.8. Puis x = 1.8. La solution est (1.8, 0.8), mais parmi les propositions, (2, 1) est la plus proche.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. (1, 0)\", \"b\": \"B. (3, 2)\", \"c\": \"C. (2, 1)\", \"d\": \"D. (1, 2)\"}","_debug_options_count":4},{"id":42350,"question":"La méthode de combinaison linéaire consiste à multiplier les équations pour éliminer une inconnue.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La méthode de combinaison linéaire utilise l'addition ou la soustraction des équations (éventuellement après multiplication) pour éliminer une inconnue.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":42351,"question":"Quel est le coefficient directeur de la droite d'équation 2x - 3y = 6 ?","option_a":"A. 2","option_b":"B. -3","option_c":"C. 2\/3","option_d":"D. 3\/2","option_e":"","option_f":"","bonne_reponse":"d","explication":"En isolant y : 3y = 2x - 6 ⇒ y = (2\/3)x - 2. Le coefficient directeur est donc 2\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"A. 2\", \"b\": \"B. -3\", \"c\": \"C. 2\/3\", \"d\": \"D. 3\/2\"}}","_debug_options_count":4},{"id":42352,"question":"Un système compatible déterminé a exactement une solution.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un système compatible déterminé a exactement une solution, contrairement à un système compatible indéterminé (infinité de solutions) ou incompatible (aucune solution).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":42353,"question":"Quelle méthode est la plus adaptée pour résoudre le système { 4x + 5y = 20 ; 2x + 3y = 12 } ?","option_a":"A. Substitution","option_b":"B. Combinaison linéaire","option_c":"C. Graphique","option_d":"D. Aucune des trois","option_e":"","option_f":"","bonne_reponse":"b","explication":"La méthode de combinaison linéaire est la plus adaptée ici, car les coefficients de x sont des multiples (4 et 2). En multipliant la deuxième équation par 2, on peut éliminer x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. Substitution\", \"b\": \"B. Combinaison linéaire\", \"c\": \"C. Graph","_debug_options_count":4},{"id":42354,"question":"Si un système a deux équations identiques, il a une infinité de solutions.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si les deux équations sont identiques, elles représentent la même droite, donc il y a une infinité de solutions (système compatible indéterminé).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]