Revision

1. Revision Looking Back:

2. Straight Line Graphs Sketching Straight Lines Graphs of the form y = mx + c are always straight lines. Because of this we only need two points to draw them. The best points to pick are where the line crosses the x and y axes. This happens when x = 0 and y = 0. (i) Sketch the graph of y = 2x – 6.

3. y x (3,0) (0,-6) Page 124 Exercise 2

4. Simultaneous Equations Simultaneous equations are pairs of equations with 2 unknowns. We have to find values for x and y that satisfy both equations. Since we are looking for values of x and y that satisfy both equations at the same time, equations like these are called simultaneous equations. By drawing graphs of these equations we can solve them by finding the point at which they intersect.

5. (i) Solve:

6. To find another point we just pick another value for x. Because we already have x = 0, it is best to pick a value far from zero so that we can get an accurate straight line.

7. The lines cross at (2,3). This gives the solution to the pair of equations.

9. The lines cross at (4,2). This gives the solution to the pair of equations.

10. Page 125 Exercise 3A and 3B

11. Solving Simultaneous Equations by Substitution Richard is twice as old as his sister Laura. Also, he is 5 years older than her. What is Richards age? Let Richard’s age = y years and Laura’s age = x years.. This gives us the following pair of simultaneous equations. The y values that satisfy these equations are the same for both equations

12. Solving this will give us Laura’s age. Since x = 5, we can substitute this value into any of the two equations to find the value of y. or Hence, Richard is 10 years old and Laura is 5 years old.

13. Solve the following pair of simultaneous equations by substitution. Hence the solution is (10 , 20)

14. Page 126 Exercise 4

15. 2 1 - 1 2 Solving Simultaneous Equations by Elimination The process of elimination is where we add or subtract the simultaneous equations in order to eliminate one of the unknowns. This leaves one equation with one unknown which is relatively easy to solve. Consider; Substitute this into equation 1. Hence the solution is (4.5 , 2.5)

16. + 2 1 1 2 Solve by elimination; Substitute this into equation 1. Hence the solution is (9 , 3)

17. Page 128 Exercise 6

18. 4 3 Elimination – a slight difficulty Here adding or subtracting will not eliminate the x or y term. Consider; Here, we chose which term to eliminate and multiply both equations so that these terms are of equal values so that when we add or subtract they will be eliminated. This will give equal x terms.

19. - 4 3 3 4 Substitute this into equation 4 Hence the solution is (1 , -2)

20. + 4 3 3 4 Solve by elimination I choose y. Which term do we want to eliminate? The x or the y? Substitute this into equation 2 Hence the solution is (5 , 0)

21. Page 129 Exercise 7A and 7B Page 130 Exercise 8

22. 2 2 1 3 - 2 3 Using Simultaneous Equations to Solve Problem On a recent visit to a book shop, John bought 1 book and 4 pens which cost him £9. His Friend James purchased 2 books and two pens which cost a total of £12. Calculate the cost of a book and a pen. Let b = the cost of a book Let p = the cost of a pen. Substitute this into equation 1. The cost of a book is £5.00 and the cost of a pen is £1.00

23. 2 1 - 2 1 5 CD’s and 2 DVD’s cost £74.95 while 1 CD and 2 DVD’s cost £38.99. Calculate the cost of a CD and DVD. Let c = the cost of a CD Let d = the cost of a DVD Substitute this into equation 2. The cost of a CD is £8.99 and the cost of a DVD is £15.00

24. Page 132 and 133 Exercise 10A and 10B Followed by the Check Up.