Mathematics · Oct / Nov 2025 · Paper 42 · Question 19
0580
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0580/42/O/N/25 © UCLES 2025 19 Solve the simultaneous equations. You must show all your working and give your answers correct to 2 decimal places. y x y x x 5 2 2 ¤ Å ¤ Å Å x ¤ ………………… y ¤ ………………… x ¤ ………………… y ¤ ………………… [6]
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3x2 – 5x – 11 [= 0] or 3y2 – 20y – 19 [= 0] −− ± − −××− [ ( )]5 ([ ]5) 2 4 3 11 × 2 3 OR 2 5 11 5 − = ± + x oe 6 3 6 x = 2.92, y = –0.84 and x = –1.25, y = 7.51 [10]
M2 M1 for 3x2 – 7x – 6 = 5 – 2x − 2 − 5 y 5 y − − or for y = 3 7 6 2 2 M2 −− + −− −
M1 for [ ( )]5 k or [ ( )]5 k oe oe × × 2 3 2 3 − 2 −××− or for ([ ]5) 4 3 11 oe OR 2 5
M1 for − x 6
B2 B1 for one correct solution for x and y or for x = 2.92 and –1.25 or for y = –0.84 and 7.51 If B0 scored and at least two method marks scored,
SC1 for correct substitution shown of both of their x-values or their y-values into y = 3x2 – 7x – 6 or y = 5 – 2x
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