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- AU Maths Extension 1
- Simultaneous Equations

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

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Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started Now- Intro Lesson2:34
- Lesson: 1a10:28
- Lesson: 1b3:19
- Lesson: 2a6:50
- Lesson: 2b6:53
- Lesson: 3a5:46
- Lesson: 3b3:20

The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.

Basic Concepts: Solving systems of linear equations by graphing, Solving systems of linear equations by elimination, Solving systems of linear equations by substitution, Solving quadratic equations by factoring, Solving quadratic equations using the quadratic formula

Related Concepts: Graphing linear inequalities in two variables, Graphing systems of linear inequalities, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities

- Introduction• The solutions to a system of equations are the points of intersection of the graphs.

• For a system consisting of a linear equation and a quadratic equation:

linear equation: $y = mx + b$

quadratic equation: $y = a{x^2} + bx + c$

There are 3 cases to consider:

case 1: 2 solutions case 2: 1 solution case 3: no solutions

- 1.
**Case 1: System with 2 Solutions**a)Solve the system:

$y = - x + 1$

$y = {x^2} + x - 2$b)Verify the solutions graphically - 2.
**Case 2: System with 1 Solution**a)Solve the system:

$2x - y = 8$

$y = {x^2} - 4x + 1$b)Verify the solutions graphically - 3.
**Case 3: System with No Solutions**a)Solve the system:

$10x + 5y + 15 = 0$

$y = {x^2} - 4x + 2$b)Verify the solutions graphically

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