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Add the equations so these terms cancel.","highlights":[{"text":"Solve the simultaneous equations","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=first_equation}{\\color{@sky}{4x+3y=18}}$"},{"latex":"$$\\htmlData{anchor=second_equation}{\\color{@orange}{x-3y=7}}$"},{"latex":"$$\\htmlData{anchor=added_equation}{\\color{@green}{5x=25}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"first_equation"},{"color":"orange","style":"text-color","anchor":"second_equation"},{"color":"green","style":"text-color","anchor":"added_equation"}],"connections":[{"to":"added_equation","from":"first_equation","color":"sky","style":"solid"},{"to":"added_equation","from":"second_equation","color":"orange","style":"solid"}]},"order":1,"title":"Add the equations","description":"Add corresponding terms on the left and add the right-hand sides. This elimination earns the first M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=equation_before_division}{\\color{@sky}{5x=25}}$"},{"latex":"$$\\htmlData{anchor=x_value}{\\color{@green}{x=5}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"equation_before_division"},{"color":"green","style":"text-color","anchor":"x_value"}],"connections":[{"to":"x_value","from":"equation_before_division","color":"sky","label":"divide both sides by 5","style":"solid"}]},"order":2,"title":"Find x","description":"Divide both sides by the coefficient of x."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=original_equation}{x-3y=7}$"},{"latex":"$$\\htmlData{anchor=substituted_equation}{\\color{@sky}{5-3y=7}}$"},{"latex":"$$\\htmlData{anchor=intermediate_equation}{\\color{@amber}{-3y=2}}$"},{"latex":"$$\\htmlData{anchor=y_value}{\\color{@green}{y=-\\dfrac{2}{3}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"substituted_equation"},{"color":"amber","style":"text-color","anchor":"intermediate_equation"},{"color":"green","style":"text-color-with-background","anchor":"y_value"}],"connections":[{"to":"substituted_equation","from":"original_equation","color":"sky","label":"substitute x = 5","style":"solid"},{"to":"intermediate_equation","from":"substituted_equation","color":"amber","label":"subtract 5","style":"solid"},{"to":"y_value","from":"intermediate_equation","color":"green","label":"divide by -3","style":"solid"}]},"order":3,"title":"Substitute for x","description":"Finding x = 5 and then substituting it into an original equation to find y earns the second M1 mark. Therefore, x = 5 and y = -2/3; stating both correct values earns A1."}]}],"generatedAt":"2026-07-20T16:31:42.626Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":31},"walkthroughVideo":null},{"id":"b36b8b68-a092-460f-baf0-55bb8d4de637","revisionId":"901d25c1-a0c1-4b7a-bbef-8561d54839a0","questionNumber":"2","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Simultaneous Equations","calculatorUse":null,"isCalculation":true,"parts":[{"id":"3dd42278-e074-4e01-b74d-361f6f9237e3","label":"0","content":"Solve the simultaneous equations\n\n$$x - 3y = -23$$\n\n$$5x + 2y = 4$$","markscheme":"- Multiplies first equation by 5 to get $5x - 15y = -115$ M1\n- Subtracts equations to find $y = 7$ M1\n- Substitutes $y=7$ to find $x = -2$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct method to eliminate one variable (e.g., multiplying first equation by 5).","code":"M"},{"id":"p2","marks":1,"description":"Finds the value of one variable ($y=7$ or $x=-2$).","code":"M"},{"id":"p3","marks":1,"description":"Correct values: $x = -2$ and $y = 7$.","code":"A"}],"finalAnswers":["x=-2, y=7"],"generatedAt":"2026-05-07T01:58:24.365Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":40},"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"8147d4f3-4573-4d0b-be74-6fadb7f7af46","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"b36b8b68-a092-460f-baf0-55bb8d4de637","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"ae7b0e73-3deb-4449-ba25-2daa95261fe6","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"a8fe2b10-0270-4cd4-abb1-7f192ef55745","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"5fa8c900-e93a-47fc-9d15-98beb1042d51","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"843797e3-c08d-4d49-ba9e-c9c84d6b1d47","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"26393c00-9646-48ae-9f1f-7cedf8bec494","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"bcbb4573-39b1-4a1a-b79b-c690ec56dea3","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c78a11c0-af48-4f4f-a023-23dfdbcb16df","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"0c738364-9c49-4262-afb5-e192b3685b8c","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"d6c4e2bd-e7e0-4b82-8177-71882f13dc11","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6586e07e-4619-4d92-9b2a-e1823a0a8881","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"d79a855f-35b0-4930-9776-902f29e2b7a4","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"13d8f2ec-aa95-4f96-9fca-b24a0f1853f0","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true}],"title":"Simultaneous Equations","topicId":"3b545d14-c506-4fed-8b22-aa23fb9e2c12","topicSidebar":"$L3a","topicSlug":"grade-5-5-8-simultaneous-equations","topicTitle":"Simultaneous Equations"}]}],"$L3b","$L3c"]}]