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Given the system of equations in two variables a_1 x+b_1 y=c_1 and a_2 x+b_2...
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You need to remember that the number of solutions to a consistent dependent system is infinite.
You also need to remember that the equations in system represent the equations of coincident lines.
You need to remember the condition of two coincident lines `a_1 x+b_1 y=c_1` and `a_2 x+b_2 y=c_2` :
`a_1/a_2 = b_1/b_2 = c_1/c_2`
You may consider as example the following system of equations such that:
`x - y = 1`
`3x - 3y =3`
You may use substitution to solve the system such that:
`x = 1+y`
`3(1+y)-3y=3 =gt 3+3y-3y=3`
Notice that using the condition between coefficients of coincident lines yields:
`1/3 = (-1)/(-3) = 1/3`
Hence, you need to consider the following condition between coefficients for the system to be consistent dependent: `a_1/a_2 = b_1/b_2 = c_1/c_2.`
Posted by sciencesolve on May 11, 2012 at 5:21 PM (Answer #1)
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