Practice

Simultaneous Linear Equations

1. Solve the following pairs of simultaneous equations using the substitution method.

(a) 2y – x = 3,3x + y = 5

(b) 3x + y = 11,5x – 4y = 7

(c) 2x + 3y = 19,10x – 2y = 10

2. Solve the following pairs of simultaneous equations using the elimination method.

(a) 2x + 3y = 3,4x + 5y = 5

(b) 3x + 5y = 30,4y – 3x = –3

(c) 7x – 2y = –7,15x – 2y = 1

(d) 5x + 3y = 26,2x + 4y = 16

3. Answer the whole of this question on a sheet of graph paper.

(a) The tables below shows the corresponding values of x and y for the equationsy – x = 1 and y + 2x = 4.

y – x = 1x –1 0 1y a b c

y + 2x = 4x –1 0 1y d e f

(i) Find the value of a, of b, of c, of d, of e and of f.(ii) Using a scale of 1 cm to represent 1 unit on both axes and on the same axes,

draw the graphs of y – x = 1 and y + 2x = 4 for –1 ≤ x ≤ 1.(iii) Hence, solve the pairs of simultaneous equations using the graphical method.

(b) The tables below shows the corresponding values of x and y for the equations2x – 3y = 6 and x – 2y = 2.

2x – 3y = 6x –3 0 3y a b c

x – 2y = 2x –3 0 3y d e f

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(i) Find the value of a, of b, of c, of d, of e and of f.(ii) Using a scale of 1 cm to represent 1 unit on both axes and on the same axes,

draw the graphs of 2x – 3y = 6 and x – 2y = 2 for –3 ≤ x ≤ 3.(iii) Hence, solve the pairs of simultaneous equations using the graphical method.

(c) The tables below shows the corresponding values of x and y for the equations3x + y = 5 and 6x + 2y = 7.

3x + y = 5x –1 0 1y a b c

6x + 2y = 7x –1 0 1y d e f

(i) Find the value of a, of b, of c, of d, of e and of f.(ii) Using a scale of 1 cm to represent 1 unit on both axes and on the same axes,

draw the graphs of 3x + y = 5 and 6x + 2y = 7 for –1 ≤ x ≤ 1.(iii) Hence, solve the pairs of simultaneous equations using the graphical method.

(d) The tables below shows the corresponding values of x and y for the equations3x – y = 1 and 2y = 6x – 2.

3x – y = 1x –1 0 1y a b c

2y = 6x – 2x –1 0 1y d e f

(i) Find the value of a, of b, of c, of d, of e and of f.(ii) Using a scale of 1 cm to represent 1 unit on both axes and on the same axes,

draw the graphs of 3x – y = 1 and 2y = 6x – 2 for –1 ≤ x ≤ 1.(iii) Hence, solve the pairs of simultaneous equations using the graphical method.

4. There are 21 cars and motorcycles altogether at a car park. Jim counted a total of 66 tyres belonging to the cars and motorcycles. How many cars and motorcycles are there respectively?

End of Practice

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