6. (a) On the grid below, draw straight lines and use shading to show the region R that satisfies the inequalities 2 + 6 x  y  x x y  (3) The point with coordinates (x, lies inside the region R. P y) and are integers. x y (b) Write down the coordinates of all the points of R whose coordinates are both integers. ................................................................................................................................................ (2) (Total 5 marks) 7. <  1 > < + 1 x y y x –2 –2 and are integers. x y On the grid, mark with a cross (), each of the six points which satisfies all these 3 inequalities. (Total 3 marks) 8. The graphs of the straight lines with equations 3y 2x 12 and 1 have been drawn on the grid. + = y = x – (a) Use the graphs to solve the simultaneous equations 3y + 2x = 12 = y x –1 ..................................... ..................................... x = y = (1) (b) 3y + 2x > 12 < 1 < 6 y x – x and are integers. On the grid, mark with a cross (×) each of the four points which satisfies all x y these 3 inequalities. (3) (Total 4 marks)
6. (a) On the grid below, draw straight lines and use shading to show the region R that satisfies the inequalities x  2 y  x x + y  6 (3) The point P with coordinates (x, y) lies inside the region R. x and y are integers. (b) Write down the coordinates of all the points of R whose coordinates are both integers. ................................................................................................................................................ (2) (Total 5 marks) 7. –2 < x  1 y > –2 y < x + 1 x and y are integers. On the grid, mark with a cross (), each of the six points which satisfies all these 3 inequalities. (Total 3 marks) 8. The graphs of the straight lines with equations 3y + 2x = 12 and y = x – 1 have been drawn on the grid. (a) Use the graphs to solve the simultaneous equations 3y + 2x = 12 y = x –1 x = ..................................... y = ..................................... (1) (b) 3y + 2x > 12 y < x – 1 x < 6 x and y are integers. On the grid, mark with a cross (×) each of the four points which satisfies all these 3 inequalities. (3) (Total 4 marks)
GCSE-InequalitiesRegionsWorksheet.docx