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

Answer: c , inconsistent

Inconsistent

If a system has no solution, it is inconsistent. The graphs of the lines do not intersect, so the graphs are parallel with no solution. so the

Step-by-step explanation:

Answer 2

Answer:

D) Consistent and Independent

Step-by-step 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 $\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

The system is consistent and dependent if $\frac{a_{1} }{a_{2}} =\frac{b_{1} }{b_{2}} =\frac{c_{1} }{c_{2}}$

The system is inconsistent if $\frac{a_{1} }{a_{2}} =\frac{b_{1} }{b_{2}} \neq \frac{c_{1} }{c_{2}}$

Now, in the given system

4x - y + 3 = 0 and

2x - y - 4 = 0

$\frac{a_{1} }{a_{2}} =\frac{4}{2} =2$

$\frac{b_{1} }{b_{2}} =\frac{-1}{-1} =1$

So, $\frac{a_{1} }{a_{2}}\neq \frac{b_{1} }{b_{2}}$

Hence, the given system is consistent and independent.