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Mathematics
Lexi Lang
16 May, 06:28
How to solve linear equations
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Matteo Decker
16 May, 08:09
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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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