Question

Which BEST describes the system of equations? y = 4x + 3 y = 2x − 4 A) Consistent B) Inconsistent C) Consistent and Dependent D) Consistent and Independent

Answer 1

D) Consistent and Independent

Explanation:

The system of equations,

`a_(1) x+b_(1) y+c_(1) =0` and

`a_(2) x+b_(2) y+c_(2) =0`

is consistent and independent if
`(a_(1) )/(a_(2)) \\eq (b_(1) )/(b_(2))`

The system is consistent and dependent if
`(a_(1) )/(a_(2)) =(b_(1) )/(b_(2)) =(c_(1) )/(c_(2))`

The system is inconsistent if
`(a_(1) )/(a_(2)) =(b_(1) )/(b_(2)) \\eq (c_(1) )/(c_(2))`

Now, in the given system

4x - y + 3 = 0 and

2x - y - 4 = 0

`(a_(1) )/(a_(2)) =(4)/(2) =2`

`(b_(1) )/(b_(2)) =(-1)/(-1) =1`

So,
`(a_(1) )/(a_(2))\\eq (b_(1) )/(b_(2))`

Hence, the given system is consistent and independent.