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29 June, 19:20

How to solve linear equations

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  1. 29 June, 19:49
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    There are many methods to solve linear equations, such as:

    1. Equating method: Let's take two simultaneous linear equations x+y=5 and x-y=1.

    x + y=5 can be written as x = 5-y ... (1)

    In the same way,

    x-y=1 or, x = 1+y ... (2)

    Here, we equate the two equations and get the value of unknowns.

    2. Substituting method: Again, take the equations x+y=5 and x-y=1.

    x+y=5

    or, x=5-y ... (1)

    x-y=1 ... (2)

    Substituting equation (1) in (2),

    (5-y) - y=1

    or, 5-2 y = 1

    or, y = 2.

    This is called substitution method.

    3. Formula method: simultaneous linear equations can also be solved by formula.

    If there are two equations: ax+by + c=0 and d x+e y+f=0 then the solution of such equation would be:

    x = (bf - e c) / (a e - db), y = (a f-dc) / (db - a e).

    For example,

    2 x + 3 y = 10 or, 2 x + 3 y-10=0 ... (1)

    x+y=-44 or, x+y+44=0 ... (2)

    Comparing equation (1) and (2) with ax+by+c = 0 and dx+ey+f=0, a=2, b=3, c=-10, d = 1, e=1, f=44.

    Using formula,

    x = - 142 and y = 98.

    4. Graphical method

    5. Elimination method

    6. Matrix method
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