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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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spock7 | Student, Undergraduate | Honors

Posted May 11, 2012 at 3:06 PM via web

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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 y=c_2...

assign possible values of a_1, b_1, c_1, a_2, b_2, c_2 to make the system consistent and dependent

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 11, 2012 at 5:21 PM (Answer #1)

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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`

`3=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.`

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