33 a They are the same equation. Multiply C1 3 C1 for clear explanation M the first equation by 3 and it is the same as the second equation, so they have an infinite number of solutions. b C1 C1 for clear explanation Treble the first equation to get 15x – 3y = 27 x They have the same coefficients of and but a different constant so they y are parallel lines with no intersections 2 and so no solutions. 34 a M1 2 M1 for equating both equations M x2 + 2x 5 = 6x 9 – – M1 3 M1 for arranging to equal 0 x2 4x + 4 = 0 M1 M1 for factorising – (x 2)(x 2) = 0 – – x = 2 A1 x A1 for = 2 cao x = 2 A1 y y = 3 A1 for = 3 cao y = 6 × 2 9 = 3 – y = 3 b C1 C1 for sketch iii There is just one intersection of the two C1 C1 for clear explanation graphs, so it has to be sketch iii, as the 7 straight line touches the curve once.
33 a b They are the same equation. Multiply the first equation by 3 and it is the same as the second equation, so they have an infinite number of solutions. Treble the first equation to get 15x – 3y = 27 They have the same coefficients of x and y but a different constant so they are parallel lines with no intersections and so no solutions. C1 C1 3 C1 for clear explanation C1 for clear explanation M 2 34 a b x2 + 2x – 5 = 6x – 9 x2 – 4x + 4 = 0 (x – 2)(x – 2) = 0 x = 2 y = 6 × 2 – 9 = 3 y = 3 There is just one intersection of the two graphs, so it has to be sketch iii, as the straight line touches the curve once. x = 2 y = 3 M1 M1 M1 A1 A1 C1 C1 2 3 M1 for equating both equations M1 for arranging to equal 0 M1 for factorising A1 for x = 2 cao A1 for y = 3 cao C1 for sketch iii C1 for clear explanation M 7
Higher_Skills_Algebra_MarkScheme_Edexcel.docx