/marks>\n- $x = -2, y = 1$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies the intersection point $(-2, 1)$ on the graph.","code":"M"},{"id":"p2","marks":1,"description":"States $x = -2$ and $y = 1$.","code":"A"}],"finalAnswers":["x=-2, y=1"],"generatedAt":"2026-05-07T01:58:34.677Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"7718de3e-839b-46c8-b4bb-aa121a5ffbc9","revisionId":"3d18073a-5a1e-4915-94d8-00a420a3505e","questionNumber":"3","questionType":"LA","specification":"The graph of $4y - 6x = 7$ is drawn on the grid.\n\n![A coordinate grid with x and y axes ranging from -3 to 3 and -7 to 7 respectively. A straight line representing the equation 4y - 6x = 7 is plotted.](img:d9d706121d1c4ba9ad2c793746382361_img.jpg)","difficulty":2,"totalMarks":4,"sourceTitle":"Solving Simultaneous Equations Graphically","calculatorUse":null,"parts":[{"id":"968e3fbf-b62a-4770-b807-cf9ecb78e08e","label":"a","content":"On the grid, draw the graph of $y = -2x$","markscheme":"- At least two correct points calculated or plotted (e.g., $(0,0), (1,-2), (2,-4)$) M1\n- Correct straight line drawn through the origin with gradient $-2$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates or plots at least two correct points for $y = -2x$.","code":"M"},{"id":"p2","marks":1,"description":"Draws a correct straight line through the origin with gradient $-2$.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-07T01:58:34.677Z","modelVersion":"gemini-3-flash-preview"}},{"id":"7f34c16f-7d04-4e7f-81d1-07acc9e71efc","label":"b","content":"Use the graphs to solve the simultaneous equations\n\n$$\\begin{aligned} 4y - 6x &= 7 \\\\ y &= -2x \\end{aligned}$$","markscheme":"- Identifies intersection point from the drawn graphs M1\n- $x = -0.5, y = 1$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies the intersection point of the two lines.","code":"M"},{"id":"p2","marks":1,"description":"States $x = -0.5$ and $y = 1$.","code":"A"}],"finalAnswers":["x=-0.5, y=1"],"generatedAt":"2026-05-07T01:58:34.677Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"ff275184-f6cd-4828-a90e-d06bd028b50b","revisionId":"ed8e3314-8149-482b-b5de-4a178359a61e","questionNumber":"4","questionType":"LA","specification":"The diagram shows two straight lines. The equation of the lines are $y = 4x - 5$ and $y = 2x + 1$.\n\n![A Cartesian coordinate system showing two intersecting straight lines.](img:e94f3bbb6f7501b9a1344dd0210e5dd8_img.jpg)","difficulty":2,"totalMarks":3,"sourceTitle":"Solving Simultaneous Equations Graphically","calculatorUse":null,"parts":[{"id":"89f8677f-02fe-466d-aaaa-9e4a227f3e7c","label":"a","content":"Work out the coordinates of the point where the line intersect.","markscheme":"- Sets equations equal: $4x - 5 = 2x + 1$ M1\n- Solves for $x$: $2x = 6 \\Rightarrow x = 3$ A1\n- Substitutes $x$ to find $y$: $y = 2(3) + 1 = 7$. Final answer $(3, 7)$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Equates the two expressions for $y$ to form an equation in $x$.","code":"M"},{"id":"p2","marks":1,"description":"Correctly solves for $x = 3$.","code":"A"},{"id":"p3","marks":1,"description":"Correctly finds $y = 7$ and gives answer as $(3, 7)$.","code":"A"}],"finalAnswers":["(3, 7)"],"generatedAt":"2026-05-07T01:58:34.677Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"a2ba7706-bcb8-4196-9f24-ceb35bbe9178","revisionId":"413bd36a-249d-40e1-8c76-0723450be8d4","questionNumber":"5","questionType":"LA","specification":"The diagram shows two straight lines. The equation of the lines are $y = 2x + 3$ and $y = -\\frac{2}{3}x + 1$.\n\n![A Cartesian coordinate system showing two intersecting straight lines.](img:b7251436a2a3c0d1c00c3e935df2a8f5_img.jpg)","difficulty":3,"totalMa