Systems of Linear Equations Module Review PDF

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Sample test for Module 8...

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Systems of Linear Equations Review 1) Solve the following 2 × 2 systems in three different ways: i) graphing ii) substitution and iii) Elimination a) 2฀฀ − 4฀ ฀ = 1 (1) 4฀฀ − 6฀ ฀ = 2 (2)

b) 2฀฀ − ฀ ฀ = 3 (1) 4฀฀ − 2฀ ฀ = 2 (2)

2) Solve the following 2 × 2 systems of equations by using a Elimination to get an exact point of intersection (if it exists). State that the lines are parallel or coincident if they do not intersect at a point. Include a check for each point of intersection. (4 marks each) CHECK a) ฀฀ − ฀฀ = 3 ฀ ฀ = −฀฀ + 5

b) 2฀ ฀ + ฀ ฀ = 1 −฀฀ − 2฀ ฀ = −5

c) 2฀ ฀ + 4฀ ฀ = 6 ฀ ฀ + 4฀ ฀ = 2

d) 4฀ ฀ + 3฀ ฀ = 2 ฀ ฀ + 2฀ ฀ = 6

CHECK e) 2฀฀ − 5฀ ฀ = 9 4฀฀ − 10฀ ฀ = 18

f) 7฀฀ − 4฀ ฀ = 13 14฀฀ − 8฀ ฀ = 17

g) 4฀ ฀ + 5฀ ฀ = 6 5฀ ฀ + 2฀ ฀ = 8

h) 3฀ ฀ + 2฀ ฀ = 19 4฀฀ − 5฀ ฀ = 10

3) Solve the following 3 × 3 systems of equations by using an algebraic method to get an exact point of intersection (if it exists). State that the geometry is parallel or coincident if they do not intersect at a point. Include a check for each point of intersection. (8 marks each) CHECK a) ฀฀ − ฀ ฀ + 5฀ ฀ = −4 5฀ ฀ + ฀฀=0 ฀ ฀ + 3฀ ฀ + ฀ ฀ = 12

b) 2฀ ฀ + 3฀ ฀ + ฀ ฀ = −6 2฀฀ − 4฀฀ − ฀ ฀ = 17 4฀ ฀ + ฀ ฀ + 4฀ ฀ = 1

CHECK c) ฀ ฀ + ฀฀ − 2฀ ฀ = 8 3฀ ฀ + ฀ ฀ = −6 2฀฀ − ฀฀ + 3฀ ฀ = −14

d) 2฀ ฀ + 8฀ ฀ + 4฀ ฀ = −24 ฀ ฀ + 4฀ ฀ + 2฀ ฀ = 4 ฀ ฀ + ฀ ฀ + ฀ ฀ = −6...