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- Simultaneous Equations

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

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Get Started Now- Intro Lesson9:21
- Lesson: 13:40
- Lesson: 23:33

Depending on whether and how the linear equations in a system touch each other, there will be different number of solutions to the system. There can be one solution, no solution and even infinite solution.

Basic Concepts: Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$, Slope intercept form: y = mx + b, Parallel line equation

Related Concepts: System of linear-quadratic equations, System of quadratic-quadratic equations, Graphing systems of linear inequalities, Graphing systems of quadratic inequalities

- Introduction$\bullet$ The solutions to a system of equations are the points of intersection of the graphs.

$\bullet$ For a system consisting of two linear equations:

There are 3 cases to consider:

- 1.State whether each of the following systems have ONE, NONE, or INFINITE solutions

i) 3x + y = 7

4x + y = 7

ii) 6x + 2y = 10

3x + y = 5

iii) x - y = 3

3x - 3y = 6 - 2.Find a value for c that will give the following system:

3y + 2cx = 6

y - 6x = 0

i) one solution

ii) no solutions

9.

Simultaneous Equations

9.1

Determining number of solutions to linear equations

9.2

Solving simultaneous linear equations by graphing

9.3

Solving simultaneous linear equations by elimination

9.4

Solving simultaneous linear equations by substitution

9.5

Money related questions in linear equations

9.6

Unknown number related questions in linear equations

9.7

Distance and time related questions in linear equations

9.8

Rectangular shape related questions in linear equations

9.9

Simultaneous linear-quadratic equations

9.10

Simultaneous quadratic-quadratic equations

9.11

Solving 3 variable simultaneous equations by substitution

9.12

Solving 3 variable simultaneous equations by elimination

9.13

Solving 3 variable simultaneous equations with no or infinite solutions

9.14

Word problems relating 3 variable simultaneous equations

We have over 1640 practice questions in AU Maths Extension 1 for you to master.

Get Started Now9.1

Determining number of solutions to linear equations

9.3

Solving simultaneous linear equations by elimination

9.4

Solving simultaneous linear equations by substitution

9.5

Money related questions in linear equations

9.6

Unknown number related questions in linear equations

9.7

Distance and time related questions in linear equations

9.8

Rectangular shape related questions in linear equations

9.9

Simultaneous linear-quadratic equations

9.10

Simultaneous quadratic-quadratic equations