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The Robert Smyth School Mathematics Faculty Topic 9 Solving Equations 2 Innovation & excellence HW3 – Grade B Simultaneous Equations y 1. The graph of 4y + 3x = 12 has been drawn on the grid below. 4 Draw another line on the grid to solve the simultaneous equations 4y + 3x = 12 3 y = 2x – 4 2 ............................................................................................................... .............................................................................................................. 1 .............................................................................................................. O Answer x = ......................., y = ………………. 1 2 3 4 (Total 3 marks) –1 2. SUPERGROW GARDEN CENTRE ROSES £x each SHRUBS £y each –2 –3 (a) Megan buys 4 roses and 3 shrubs. She pays £33. Use this information to write down an equation in x and y. –4 ..................................................................................................................................... (1) (b) Josh buys 6 roses and 6 shrubs. He pays £57. Use this information to write down another equation in x and y. ..................................................................................................................................... (1) (c) Solve your equations simultaneously to find the values of x and y. You must show your working. Do not use trial and improvement. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer x = .......................... , y = ............................... (3) The Robert Smyth School (Total 5 marks) 1 x The Robert Smyth School Mathematics Faculty Topic 9 Solving Equations 2 Innovation & excellence 3. Solve the simultaneous equations 4x + 3y = 5 2x – 5y = 9 You must show your working. Do not use trial and improvement. ......................……….............................................................................................................. ......................……….............................................................................................................. ......................……….............................................................................................................. ......................……….............................................................................................................. ......................……….............................................................................................................. ......................……….............................................................................................................. ......................……….............................................................................................................. ......................……….............................................................................................................. Answer x = ....................... , y = .......................... (Total 4 marks) 4. Solve these simultaneous equations x + 3.6y = 2 x – 2.4y = 5 You must show all your working. Do not use trial and improvement. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer x = …………………………….. y = …………………………….. (Total 3 marks) The Robert Smyth School 2 The Robert Smyth School Mathematics Faculty Topic 9 Solving Equations 2 Innovation & excellence 5. Solve the simultaneous equations 2x + 3y = 9 3x + 2y = 1 You must show your working. Do not use trial and improvement. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................................. Answer x = ..................., y = ............................. (Total 4 marks) 6. Solve these simultaneous equations 5x + 3y = 6 3x – 7y = 19 You must show your working. Do not use trial and improvement. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer x = ......................... , y = ........................... (4) (Total 5 marks) The Robert Smyth School 3 The Robert Smyth School Mathematics Faculty Topic 9 Solving Equations 2 Innovation & excellence 1. 2 points from (0, –4) (1, –2) (2, 0) (3, 2) (4, 4) May not be seen, so may be inferred from Al below Ml Segment of correct line intersecting given line Al x = 2.55, y = 1.1 A1 Each ±0.1 [3] 2. (a) 4x + 3y = 33 B1 Ignore £ signs (b) (c) 6x + 6y = 57 Note: 4x + 3y and 6x + 6y without right hand side... B1 SC1 Equalised coefficients Lhs correct + attempt to multiply either rhs x = 4.5 M1 y=5 A1ft x = 4.5 and y = 5 with no working... or by trial and improvement SC1 SC1 [4] 3. 4x – 10y = 18 20x + 15y = 25 6x – 15y = 27 Allow 1 error on any method for 1st M1 5 – 4x Substitution: eg y = 3 13y = –13 26x = 52 Correct elimination from their equations 5 – 4x Substitution: eg 2x – 5 =9 3 y = –1 x=2 x=2 y = –1 ft on a correct given equation SC1 x = 2, y = –1 no working or trial and improvement M1 M1 dep A1 B1 ft [4] 4. trial and improvement is 0 1st-2nd M1 6y = – 3 allow 1 error eg, 12y = – 3 6y = 3 2 – 3.6y = 5 + 2.4y allow 1 error or 2.4equation(l) + 3.6equation(2) The Robert Smyth School 4 The Robert Smyth School Mathematics Faculty Topic 9 Solving Equations 2 Innovation & excellence y = – 0.5 or x = 3.8 A1 y = – 0.5 and x = 3.8 Must have both. Allow reversed if both seen correct in working ft if Ml awarded Alft [3] 5. 6x + 9y = 27 6x + 4y = 2 4x + 6y = 18 9x + 6y = 3 5y = 25 or 5x = – 15 Allow total of 1 error on 1st or 2nd method marks y = 5 or x = – 3 M1 M1 dep A1 x = –3 and y = 5 A1 Correct answer with no working or using T & I scores SC1 [4] 6. Attempt to rearrange one equation and substitute into another or Attempt to balance x or y and eliminate eg 15x + 9y = 18 15x 35y = 95 followed by an attempt to subtract eg 44y = –77 35x + 21y = 42 9x – 21y = 57 followed by an attempt to add eg 44x = 99 M1 Solving resultant equation to find x = 2.25 or y = –1.75 A1 Attempt to eliminate other variable or substitution of found value into one of their equations eg 11.25 + 3y = 6, 5x – 5.25 = 6 M1 Solving to find another value y = –1.75 or x = 2.25 A1 [5] The Robert Smyth School 5
