Everything Maths Grade 11

9.3 CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS

10

20

30

40

8 6 − 4 − − 2 − 2 4 6 8

y=

− 3

x+

9

y

=

x

2 −

9

�

�

(−6;27)

(3;0)

Step 3 : Find the intersection of the graphs.

The graphs intersect at (−6;27) and at (3;0).

Step 4 : Write the solution ofthe system of simultaneous equations as given by the

intersection of the graphs.

The first solution is x =− 6 and y = 27. The second solution is x = 3 and y = 0.

Exercise 9 - 1

Solve the following systems of equations graphically. Leave your answerin surd form, where appropri-

ate.

1. b^2 − 1 − a = 0; a + b− 5 = 0


2. x + y− 10 = 0; x^2 − 2 − y = 0


3. 6 − 4 x− y = 0;12− 2 x^2 − y = 0


4. x + 2y− 14 = 0; x^2 + 2− y = 0


5. 2 x + 1− y = 0;25− 3 x− x^2 − y = 0

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 01ad (2.) 01ae (3.) 01af (4.) 01ag (5.) 01ah

9.3 Algebraic Solution EMBAR

The algebraic method of solving simultaneous equations is by substitution.