EQUATIONS and INEQUALITIES



EQUATIONS and INEQUALITIES

SIMULTANEOUS EQUATIONS

There are two methods: elimination and substitution.

ELIMINATION

Example

Solve the equations

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Ex 3A

SUBSTITUTION

Example

Solve the equations

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Substitute the first equation into the second to obtain an equation only involving x.

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You may need to rearrange one of the equations first.

Ex 3B

QUADRATIC SIMULTANEOUS EQUATIONS

Substitute the linear equation into the quadratic equation.

Sometimes answers may be left in surd form.

Example

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Ex 3C

LINEAR INEQUALITIES

These can be solved in the same way as equations.

i.e. perform the same operation on both sides.

The only difference is when you multiply or divide by a negative quantity, you must reverse the “truth” of the inequality

i.e. < becomes >, ≥ becomes ≤ etc.

Example

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Example

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[pic]Ex 3D

QUADRATIC INEQUALITIES

Factorise the quadratic

Sketch the quadratic curve

Use the sketch to solve the inequality

Example

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Ex 3E

-----------------------

y

x

0

-3

-2

-1

7

6

5

4

3

2

1

-10

-5

10

5

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