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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

4.

Systems of Equations

4.1

Determining number of solutions to linear equations

4.2

Solving systems of linear equations by graphing

4.3

Using elimination method to solve systems of equations

4.4

Using substitution method to solve systems of equations

4.5

Money related questions in linear equations

4.6

Unknown number related questions in linear equations

4.7

Distance and time related questions in linear equations

4.8

Rectangular shape related questions in linear equations

4.9

System of quadratic-quadratic equations

4.10

Solving 3 variable systems of equations by substitution

4.11

Solving 3 variable systems of equations by elimination

4.12

Solving 3 variable systems of equations with no solution, infinite solutions

4.13

Word problems relating 3 variable systems of equations

We have over 1060 practice questions in Algebra 2 for you to master.

Get Started Now4.1

Determining number of solutions to linear equations

4.3

Using elimination method to solve systems of equations

4.4

Using substitution method to solve systems of equations

4.5

Money related questions in linear equations

4.6

Unknown number related questions in linear equations

4.7

Distance and time related questions in linear equations

4.8

Rectangular shape related questions in linear equations

4.9

System of quadratic-quadratic equations