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

Question

asked Sep 12, 2020 160k views

1 Answer

TheJacobTaylor · Answer 1 · 2020-09-18T11:34:43+0000

Answer:

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.