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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:

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

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

8.

Simultaneous Equations

8.1

Determining number of solutions to linear equations

8.2

Solving simultaneous linear equations by graphing

8.3

Solving simultaneous linear equations by elimination

8.4

Solving simultaneous linear equations by substitution

8.5

Money related questions in linear equations

8.6

Unknown number related questions in linear equations

8.7

Distance and time related questions in linear equations

8.8

Rectangular shape related questions in linear equations

8.9

Simultaneous linear-quadratic equations

8.10

Simultaneous quadratic-quadratic equations

8.11

Solving 3 variable simultaneous equations by substitution

8.12

Solving 3 variable simultaneous equations by elimination

8.13

Solving 3 variable simultaneous equations with no or infinite solutions

8.14

Word problems relating 3 variable simultaneous equations

We have over 600 practice questions in AU General Maths for you to master.

Get Started Now8.1

Determining number of solutions to linear equations

8.3

Solving simultaneous linear equations by elimination

8.4

Solving simultaneous linear equations by substitution

8.5

Money related questions in linear equations

8.6

Unknown number related questions in linear equations

8.7

Distance and time related questions in linear equations

8.8

Rectangular shape related questions in linear equations

8.9

Simultaneous linear-quadratic equations

8.10

Simultaneous quadratic-quadratic equations