Answer:
D) Consistent and Independent
Step-by-step explanation:
The system of equations,
[tex]a_{1} x+b_{1} y+c_{1} =0[/tex] and
[tex]a_{2} x+b_{2} y+c_{2} =0[/tex]
is consistent and independent if [tex]\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}[/tex]
The system is consistent and dependent if [tex]\frac{a_{1} }{a_{2}} =\frac{b_{1} }{b_{2}} =\frac{c_{1} }{c_{2}}[/tex]
The system is inconsistent if [tex]\frac{a_{1} }{a_{2}} =\frac{b_{1} }{b_{2}} \neq \frac{c_{1} }{c_{2}}[/tex]
Now, in the given system
4x - y + 3 = 0 and
2x - y - 4 = 0
[tex]\frac{a_{1} }{a_{2}} =\frac{4}{2} =2[/tex]
[tex]\frac{b_{1} }{b_{2}} =\frac{-1}{-1} =1[/tex]
So, [tex]\frac{a_{1} }{a_{2}}\neq \frac{b_{1} }{b_{2}}[/tex]
Hence, the given system is consistent and independent.
