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
  • 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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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
GCE N(A)-Level Maths