Solving systems of linear equations by graphing

Solving systems of linear equations by graphing

In order to determine the number of solutions to a system of linear equations, other than by finding the slope of the lines, we can also graph the equations out and look for the intersection of the lines.
Basic Concepts: Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}, Slope intercept form: y = mx + b, Graphing linear functions using various forms, Determining number of solutions to linear equations
Related Concepts: System of linear equations, System of linear-quadratic equations, Graphing systems of linear inequalities, Graphing systems of quadratic inequalities

Lessons

One Solution: Two linear equations intersect at one point. It is a consistent system of independent equation.
system of linear equations with one solution
No Solution:Two linear equations are parallel to each other. It is an inconsistent system.
system of linear equations with two solutions
Infinite Solution:
system of linear equations with infinite solution
  • Introduction
    a)
    How to find the number of solutions to systems of linear equations?

    b)
    How to solve systems of linear equations by graphing?

  • 1.
    Graph the following linear equations and find the point of intersection. State the consistency.
    a)
    2x - y = - 9
    x + 3y = 6

    b)
    2x + 2y = 8
    3x - y = 0

    c)
    4x + 6y = 12
    2x + 3y = 9

    d)
    y - x = 2
    4y - 8 = 4x

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9.
Solving Simultaneous Equations
9.1
Determining number of solutions to linear equations
9.2
Solving simultaneous equations by graphing
9.3
Solving simultaneous equations by elimination
9.4
Solving simultaneous equations by substitution
9.5
Money related questions in linear equations
9.6
Unknown number related questions in linear equations
9.7
Distance and time related questions in linear equations
9.8
Rectangular shape related questions in linear equations
AU Year 10 Maths