A linear equation is an equation containing one or more variables and constant(s), where the highest degree of the terms in the equation is 1.
A simultaneous Linear Equation is an equation containing 2 or more linear equations.
For instance, x+4y=2 and x+y=5 are simultaneous linear equations.
To solve for nnumber of variables, we need n number of consistent and independent equations.
3.1.1 Dependent Equations
These are equations that can be derived or deduced from other equations. They do not provide any new information.
For instance if the 2 equations are x+2y=5 -----Eq(1) 2x+4y=10 -----Eq(2)
then Eq(1) ×2= Eq(2). Therefore, solving these will give us infinite values where range is not defined.
Other examples are as follows 6x+4y=20a+2b+c=11 2y=10−3x and 6a+8b−c=82 4a+4b−3c=60
3.1.2 Inconsistent Equations
These equations are two or more linear equations that have no solutions.
For instance if the 2 equations are
x+2y=5 -----Eq(1) 2x+4y=8 -----Eq(2)
Note that Eq(1) ×2=2x+4y=10.
Whereas Eq(2) is 2x+4y=8
As two values are not possible for a given expression, these equations cannot be solved.
Another example is 2x+3y=10 and 4x=18−6y
3.1.3 Consistent and Independent Equations
These are equations that have solutions. All other equations come under this category. To solve for nvariables, we need nconsistent and independent equations. The rest of this lesson covers these equations and methods to solve them.
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