Practice questions 2.6


1. Use a graphical method to solve each pair of simultaneous equations. (i) y = 3x + 4 y = 2x + 5


(ii) y = x + 3 y = 2x + 1


(ii) y = x − 3 y + x + 1 = 0


(ii) x + y = 63 x − y = 29


(iii) y = 2x + 3 y = 4x + 1


2. Use a graphical method to solve each pair of simultaneous equations. (i) y = x − 3 y = −3x + 1


(iii) y = x x + y = 2


3. Use the elimination method to solve each pair of simultaneous equations. (i) x + y = 15 x − y = 1


(iii) 3x + 3y = 51 x − 3y = 5


4. Use the elimination method to solve each pair of simultaneous equations. (i) 2x + y = 7 x + 2y = 11


(ii) 5x + 2y = 10 4x + 3y = 15


(ii) 3


__ 4 x + y = 12


__ 2 y = 1


−1 __


(ii) x x


(iii) 7x − y = 51 2x − 3y = −18


5. Use the elimination method to solve each pair of simultaneous equations. (i) 5x − y = 31


x − 3 3 x − y = −2


__ 2 + y


_ 5 + y


__ 3 = −4


_ 5 = −2


(iii) 2x + 3y = 24 1


__ 2 x − 3


__ 2 y = 3


(iii) 2x+y = 1 1


_ 2 x + 3


__ 2


6. Use the elimination method to solve each pair of simultaneous equations. (i) 3·5x+2·5y = 17 −1·5x−7·5y = −33


_ 2 y = 6·5


(iv) y = 3x + 2 y = x + 3


(iv) x + y = 1 2x + y = 3


(iv) 3x + y = 68 2x − y = 7


(iv) 5x + 2y = 41 2x − 2y = 8


(iv) 2x − y = 18 x


_ 3 − y


_ 4 = 2


(iv) 1·5x+1·5y = 25·5 x−3y=5


7. The sum of two numbers is 361. One number is 43 less than the other number. By letting the smaller number be x and the larger number be y, we can represent this information by the equations x + y = 361 and x = y − 43. Using the two equations, find the value of the two numbers.


8. The sum of two numbers is 23. The difference between the same two numbers is 15. If x is the larger number and y is the smaller number:


(i) write two equations in terms of x and y to represent this information (ii) solve these equations to find the two numbers.


9. The sum of two numbers is 98. The difference between the same two numbers is 20. If x is the larger number and y is the smaller number:


(i) write two equations in terms of x and y to represent this information (ii) solve these equations to find the two numbers.


10. The sum of two numbers is 74. The difference between the same two numbers is 60. If x is the larger number and y is the smaller number:


(i) write two equations in terms of x and y to represent this information (ii) solve these equations to find the two numbers.


11. A cinema trip for 2 adults and 2 children costs €40. A cinema trip for 1 adult and 5 children costs €52.


(i) By letting a be the cost of an adult ticket and c the cost of a child’s ticket, form two equations in terms of a and c to represent this information.


(ii) Hence, solve these equations to find the cost of a cinema ticket for an adult and the cost for a child. 46 Linking Thinking 2


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