Everything Maths Grade 11

CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS 9.2

2

4

6

− 2

− 4

− 6

− 8

− 10

− 12

− 14

6 4 − − 2 − 2 4 6

y=

2 x

−

4

y

=

4

−

x

2

(−4;−12)

(2;0)

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The parabola and the straight line intersect at twopoints: (2;0) and(−4;−12). Therefore, the solutions
to the system of equations in (9.1) is x = 2; y = 0 and x =−4; y = 12

Example 1: Simultaneous Equations

QUESTION

Solve graphically:

y− x^2 + 9 = 0

y + 3x− 9 = 0

SOLUTION

Step 1 : Make y the subject of the equation

For the first equation:

y− x^2 + 9 = 0

y = x^2 − 9

and for the second equation:

y + 3x− 9 = 0

y =− 3 x + 9

Step 2 : Draw the graphs corresponding to each equation.