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Determining number of solutions to linear equations
- Intro Lesson9:21
- Lesson: 13:40
- Lesson: 23:33
Determining number of solutions to linear equations
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=x2−x1y2−y1, 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
Lessons
- Introduction∙ The solutions to a system of equations are the points of intersection of the graphs.
∙ 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
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17.
Simultaneous Equations
17.1
Determining number of solutions to linear equations
17.2
Solving simultaneous linear equations by graphing
17.3
Solving simultaneous linear equations by elimination
17.4
Solving simultaneous linear equations by substitution
17.5
Money related questions in linear equations
17.6
Unknown number related questions in linear equations
17.7
Distance and time related questions in linear equations
17.8
Rectangular shape related questions in linear equations
17.9
Simultaneous linear-quadratic equations
17.10
Simultaneous quadratic-quadratic equations
17.11
Solving 3 variable simultaneous equations by substitution
17.12
Solving 3 variable simultaneous equations by elimination
17.13
Solving 3 variable simultaneous equations with no solution, infinite solutions
17.14
Word problems relating 3 variable simultaneous equations
Don't just watch, practice makes perfect
Practice topics for Simultaneous Equations
17.1
Determining number of solutions to linear equations
17.3
Solving simultaneous linear equations by elimination
17.4
Solving simultaneous linear equations by substitution
17.5
Money related questions in linear equations
17.6
Unknown number related questions in linear equations
17.7
Distance and time related questions in linear equations
17.8
Rectangular shape related questions in linear equations
17.9
Simultaneous linear-quadratic equations
17.10
Simultaneous quadratic-quadratic equations