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- GCE O-Level A Maths
- Simultaneous Equations

Still Confused?

Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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Get Started Now- Intro Lesson2:46
- Lesson: 19:28
- Lesson: 25:22
- Lesson: 33:19
- Lesson: 44:04

The solutions to a system of equations are the points of intersection of the lines. For a system with two quadratic equations, there are 4 cases to consider: 2 solutions, 1 solution, no solutions, and infinite solutions.

Basic concepts: System of linear-quadratic equations, 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 two quadratic equations:

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

quadratic equation: $y = d{x^2} + ex + f$

There are 4 cases to consider:case 1: 2 solutions case 2: 1 solution case 3: no solutions case 4: infinite solutions

- 1.
**Case 1: System with 2 Solutions**

Solve the system, then verify the solutions graphically:

$y = {x^2} - 6x + 5$

$y = - 2{x^2} + 9x - 7$

- 2.
**Case 2: System with 1 Solution**

Solve the system, then verify the solutions graphically:

$y = 2{x^2} + 6x + 7$

$y = - {x^2} + 4$

- 3.
**Case 3: System with No Solutions**

Solve the system, then verify the solutions graphically:

$y = - {x^2} + 6x - 10$

$y = 2{x^2} + 6x + 5$

- 4.
**Case 4: System with Infinite Solutions**

Solve the system, then verify the solutions graphically:

${x^2} - 4x - y + 3 = 0$

$5y - 5{x^2} + 20x - 15 = 0$

12.

Simultaneous Equations

12.1

Determining number of solutions to linear equations

12.2

Solving simultaneous linear equations by graphing

12.3

Solving simultaneous linear equations by elimination

12.4

Solving simultaneous linear equations by substitution

12.5

Money related questions in linear equations

12.6

Unknown number related questions in linear equations

12.7

Distance and time related questions in linear equations

12.8

Rectangular shape related questions in linear equations

12.9

Simultaneous linear equations

12.10

Simultaneous linear-quadratic equations

12.11

Simultaneous quadratic-quadratic equations

We have over 1460 practice questions in GCE O-Level A Maths for you to master.

Get Started Now12.1

Determining number of solutions to linear equations

12.3

Solving simultaneous linear equations by elimination

12.4

Solving simultaneous linear equations by substitution

12.5

Money related questions in linear equations

12.6

Unknown number related questions in linear equations

12.7

Distance and time related questions in linear equations

12.8

Rectangular shape related questions in linear equations

12.10

Simultaneous linear-quadratic equations

12.11

Simultaneous quadratic-quadratic equations