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    U1l1t Solving by Graphing

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    U1l1t Solving by Graphing

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    math
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    5 views3 pages

    U1l1t Solving by Graphing

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    math

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    © All Rights Reserved
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    Download as pdf or txt
    of 3

    L1 – Solving Linear Systems by GRAPHING Unit 1

    MPM2D
    Jensen

    Linear System: Two or more linear equations that are considered at the same time.

    Point of Intersection: The point where 2 or more lines cross.

    To solve a linear system means to find the values of the variables that satisfy ALL of the equations in the
    system. Graphically speaking, this means you will find the ordered pair (𝑥, 𝑦) where the lines intersect.

    There are 3 main methods for solving a linear When solving by graphing, you can graph the lines
    system: by:

    1) Graphing 1) Using the slope and 𝑦-intercept (rearrange in to


    2) Substitution 𝑦 = 𝑚𝑥 + 𝑏 form)
    3) Elimination 2) Use the 𝑥 and 𝑦 intercepts of each line
    3) Create a table of values for each equation

    A linear system could have 1, 0, or infinitely many solutions:

    Graph Slopes of Lines Intercepts Number of Solutions


    Intersecting

    Usually different
    DIFFERENT unless the lines 1
    intersect on an axis

    Parallel & Distinct

    Same Different 0

    Parallel & Coincident

    Same Same Infinitely Many


    Steps for Solving a Linear System by GRAPHING

    1) Rearrange the equations in to slope 𝑦-intercept form (𝑦 = 𝑚𝑥 + 𝑏)

    2) Graph equations and find the point of intersection

    3) Verify that the point of intersection satisfies the equation of both lines

    4) Clearly communicate your solution

    Example 1: Find the point of intersection of the graphs of the following systems of equations.

    a) ℓ1 : 𝑦 = 𝑥 + 4
    ℓ2 : 𝑦 = −𝑥 + 2

    b) ℓ1 : 2𝑥 + 𝑦 = 5
    ℓ2 : 𝑥 − 2𝑦 = 10
    c) ℓ1 : 2𝑥 + 5𝑦 = −20
    ℓ2 : 5𝑥 − 3𝑦 = −15

    Note: Our solution to this


    system is an estimate. The
    solution will not exactly
    verify the original equations
    but should be close!

    d) ℓ1 : 𝑦 = 2𝑥 + 3
    ℓ2 : 𝑦 = 2𝑥 − 4

    Notice the functions


    have the same slope but
    different y-intercepts.
    They will be parallel but
    distinct.

    e) ℓ1 : 𝑥 + 𝑦 = 3
    ℓ2 : 2𝑥 + 2𝑦 = 6

    Notice the lines have the


    same slope and same y-int.
    They will be parallel and
    coincident

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