EQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES
SIMULTANEOUS EQUATIONS
There are two methods: elimination and substitution.
ELIMINATION
Example
Solve the equations
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[pic] [pic]
[pic] √
Ex 3A
SUBSTITUTION
Example
Solve the equations
[pic]
Substitute the first equation into the second to obtain an equation only involving x.
[pic]
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
[pic]
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
[pic]
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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[pic]
Ex 3E
-----------------------
y
x
0
-3
-2
-1
7
6
5
4
3
2
1
-10
-5
10
5
................
................
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