2na simultaneous linear equations 2

Homework

Simultaneous Linear Equations

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

(a) 4x + y = 9,5x + 6y = 16

(b) 5x + 2y = 29,8y – x = 11

(c) 2x + 5y = 19,3x + 2y = 12

(d) 3y – 7x = –5,8y + 2x = 28

(e) 13x + 9y = 1,5x – 2y = –16

(f) 10x + 3y = –1,11x – 7y = –32

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

(a) 3x + 2y = 29,9x + 2y = 59

(b) 5y – 2x = 15,8y + 2x = 76

(c) 7x + 5y = 24,8y – 7x = 2

(d) 2x + 10y = –34,10y – 9x = –12

(e) 6x – 5y = 3,11y – 3x = 24

(f) 9x + 7y = –48,14y – 5x = –27

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 = 4 and y – 2x = 1.

y + x = 4x –1 0 1y a b c

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

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(b) The table below shows the corresponding values of x and y for the equationy + 2 = x.

x –1 0 1y a b c

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

draw the graphs of y – 2 = 0 and y + 2 = x for –1 ≤ x ≤ 1.(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 = 3 and x – 2y = –6.

3x + y = 3x –1 0 1y a b c

x – 2y = –6x –1 0 1y d e f


draw the graphs of 3x + y = 3 and x – 2y = –6 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 equations2y + 8 = x and 2y + x + 4 = 0.

2y + 8 = xx –1 0 1y a b c

2y + x + 4 = 0x –1 0 1y d e f


draw the graphs of 2y + 8 = x and 2y + x + 4 = 0 for –1 ≤ x ≤ 1.(iii) Hence, solve the pairs of simultaneous equations using the graphical method.

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(e) The tables below shows the corresponding values of x and y for the equations2x + y = 4 and y = –2x + 1.

2x + y = 4x –1 0 1y a b c

y = –2x + 1x –1 0 1y d e f


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

(f) The tables below shows the corresponding values of x and y for the equations2y – x = 2 and y = ½x + 1.

2y – x = 2x –2 0 2y a b c

y = ½x + 1x –2 0 2y d e f


draw the graphs of 2y – x = 2 and y = ½x + 1 for –2 ≤ x ≤ 2.(iii) Hence, solve the pairs of simultaneous equations using the graphical method.

4. The difference between two numbers is 55. Their sum is 259. Find the two numbers.

5. 11 years from now, Jeremy will be 4 times as old as Derek. The sum of their present ages is 43 years old. How old is Jeremy now?

6. Mrs Koh bought 4 apples and 7 pears from a fruit stall for $9.50. Mrs Wu bought 6 apples and 3 pears from the same stall for $7.50. Find the cost of 1 apple.

7. 4 hours of tennis lessons and 3 hours of swimming lessons cost $305. 6 hours of tennis lessons and 2 hours of swimming lessons cost $370. How much do 2 hours of tennis lessons cost?

8. Given that ΔABC is an equilateral triangle, find its perimeter.

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CB

A

(2x + y) cm

(x + 3y) cm

(3x – 2) cm

9. In the diagram below, ABCD is a parallelogram. Find its perimeter.

End of Homework

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(2y – 3) cm

(4y – 5) cm

(x + y + 1) cm

(5x + 2y) cm

CD

BA

2na simultaneous linear equations 2

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