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- Solving Simultaneous Equations

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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

10.

Solving Simultaneous Equations

10.1

Determining number of solutions to linear equations

10.2

Solving simultaneous equations by graphing

10.3

Solving simultaneous equations by elimination

10.4

Solving simultaneous equations by substitution

10.5

Money related questions in linear equations

10.6

Unknown number related questions in linear equations

10.7

Distance and time related questions in linear equations

10.8

Rectangular shape related questions in linear equations

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now10.1

Determining number of solutions to linear equations

10.3

Solving simultaneous equations by elimination

10.4

Solving simultaneous equations by substitution

10.5

Money related questions in linear equations

10.6

Unknown number related questions in linear equations

10.7

Distance and time related questions in linear equations

10.8

Rectangular shape related questions in linear equations