Determining number of solutions to linear equations

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=y2−y1x2−x1m = \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

Lessons

  • 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: System of linear equations
    There are 3 cases to consider:
    Graphs of system of linear equations with different number of solutions
  • 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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8.
Solving Simultaneous Equations
8.1
Determining number of solutions to linear equations
8.2
Solving simultaneous equations by graphing
8.3
Solving simultaneous equations by elimination
8.4
Solving simultaneous 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
Higher 2 Maths
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