>\n- Subtracts equations to get $13y = 39$, so $y = 3$ A1\n- Substitutes $y = 3$ into an equation to find $x = -2$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct method to eliminate x or y, such as multiplying the first equation by 2.","code":"M"},{"id":"p2","marks":1,"description":"Correct value for y ($y = 3$).","code":"A"},{"id":"p3","marks":1,"description":"Correct value for x ($x = -2$).","code":"A"}],"finalAnswers":["x = -2, y = 3"],"generatedAt":"2026-05-06T14:06:26.282Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"elimination","label":"Elimination","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=first_equation}{x-5y=-17}$"},{"latex":"$$\\htmlData{anchor=doubled_equation}{2x-10y=-34}$"}],"connections":[{"to":"doubled_equation","from":"first_equation","color":"sky","label":"multiply every term by 2"}]},"order":0,"title":"Multiply the first equation","description":"Multiply every term in the first equation by 2. Writing the resulting equation earns the M1 method mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=subtraction}{(2x+3y)-(2x-10y)=5-(-34)}$"},{"latex":"$$\\htmlData{anchor=simplified}{13y=39}$"}],"connections":[{"to":"simplified","from":"subtraction","color":"sky","label":"simplify"}]},"order":1,"title":"Subtract the equations","description":"Subtract the doubled first equation from the second equation. Writing the subtraction explicitly shows why the x terms cancel and why the right-hand side is 39."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=y_equation}{13y=39}$"},{"latex":"$$\\htmlData{anchor=y_value}{y=3}$"}],"connections":[{"to":"y_value","from":"y_equation","color":"green","label":"divide both sides by 13"}]},"order":2,"title":"Solve for y","description":"Divide both sides by 13. Reaching y = 3 from 13y = 39 earns the first A1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x-5y=-17$"},{"latex":"$$\\htmlData{anchor=substituted}{x-5(3)=-17}$"},{"latex":"$$\\htmlData{anchor=product}{x-15=-17}$"},{"latex":"$$\\htmlData{anchor=x_value}{x=-2}$"}],"connections":[{"to":"product","from":"substituted","color":"orange","label":"multiply -5 by 3"},{"to":"x_value","from":"product","color":"green","label":"add 15 to both sides"}]},"order":3,"title":"Substitute to find x","description":"Substitute y = 3 into the first original equation. Multiplying -5 by 3 gives -15; then add 15 to both sides. Reaching x = -2 earns the final A1 mark."}]}],"generatedAt":"2026-07-20T11:08:15.494Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"e2360efa-d114-4f21-9fab-1bcc830f8853","revisionId":"9dc93c3f-fa2e-4cb3-800d-28125c5528f4","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"b5e5fae5-be4e-4e24-8db2-2b3b1e5691d0","label":"a","content":"Solve the simultaneous equations\n\n$$5x + y = 17$$\n\n$$3x + 2y = 13$$","markscheme":"- Multiplies first equation by 2 to get $10x + 2y = 34$ M1\n- Subtracts equations to find $7x = 21$ or $x = 3$ A1\n- Substitutes $x = 3$ to find $y = 2$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Multiplies first equation by 2 to get $10x + 2y = 34$ (or correct method to eliminate a variable)","code":"M"},{"id":"p2","marks":1,"description":"Subtracts equations to correctly find $x = 3$","code":"A"},{"id":"p3","marks":1,"description":"Substitutes $x = 3$ into either equation to correctly find $y = 2$","code":"A"}],"finalAnswers":["x = 3, y = 2"],"generatedAt":"2026-05-06T14:06:29.949Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"elimination","label":"Elimination","steps":[{"type":"text","order":0,"title":"Choose what to eliminate","content":"The co

Simultaneous Equations Questions

Simultaneous Equations Questions

Simultaneous Equations Questions

Simultaneous Equations Questions