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Mathematics 2 ESO – Unit 8 SYSTEMS OF LINEAR EQUATIONS Page 87 – Activity 45

a) Which of these pairs of values is a solution to the equation: 2x – 3y = –7

  • I) x = 4  ;  y = 1
  • II) x = –2  ;  y = 1
  • III) x = –1  ;  y = 0
  • IV) x = 0  ;  y = 0

b) Which of these pairs of values is a solution to equation –x + y = 1

  • I) x = 4  ;  y = 1
  • II) x = –2  ;  y = 1
  • III) x = –1  ;  y = 0
  • IV) x = 0  ;  y = 0

c) Give five possible solutions to the equation 2x + 3y = 5

  1. d) Complete the table with solutions to equation: x – 3y = 2
x 10 9 –4 0 1
y 6 7 –8 12 10

 

  1. e) Complete the table with solutions to equation x – 3y = 2 and draw the graph.
x –4 –3 –2 –1 0 1 2 3 4
y

f) Watch the video on “How to Graph a Linear Equation by Finding the Intercepts“. Then graph (draw) these equations:

  • I) 4x – 4y = 6
  • II) –x – 9y = 0
  • III) –3x + 7y = 3
  • IV) x + 15y = 8

g) Draw the graph and write the solution:

  • I) 2x – y = 6   ;   –x + y = 3
  • II) –x – 4y = 5   ;   6x – 7y = 7
  • III) –2x + 7y = 9   ;   –2x + 3y = 0
  • IV) x + 4y = 6   ;   –5x + 5y = 15

h) Watch the video on “Simultaneous Equations – simple, linear, worked example“. Then solve by substitution and check the solution:

  • I) x – 4y = 3   ;   x + 8y = 3
  • II) – x – 4y = -5   ;   2x –  4y = -2
  • III) 2x + y = 4   ;   – 5x + 3y = 1
  • IV) 3x + y = 9   ;   – 12x + y = -21

i) Solve by substitution:

  • I) x – 2y = –1   ;   x + 8y = 9
  • II) – x – 4y = 6   ;   x –  4y = 10
  • III) – 2x + 7y = 0   ;   – 5x + 3y = 0
  • IV) x + 4y = –7   ;   – 2x + 3y = –8

j) Watch the video on “Simultaneous Equations – simple, linear, worked example“. Then solve by elimination and check the solution:

  • I) 2x – 6y = -4   ;   –x + 2y = 1
  • II) – 3x – 4y = –14   ;   x –  7y = –12
  • III) – 2x + 7y = 6   ;   – 2x + 3y = 0
  • IV) 2x + 4y = –8   ;   – 2x + y = –2