Respuesta :
Answer:
The correct option is A. 18x - 6y = 20
Step-by-step explanation:
A system of two equations has no solution if the lines having these equations are parallel to each other.
Also, two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] are parallel,
If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
While,
They coincide ( infinitely many solution ) if [tex]\frac{a_1}{a_2}=\frac{ b_1}{b_2}=\frac{c_1}{c_2}[/tex],
They are non parallel ( a unique solution ) if [tex]\frac{a_1}{a_2}\neq \frac{ b_1}{b_2}\neq \frac{c_1}{c_2}[/tex],
Here, the given equation,
-9x + 3y = 12
Since in lines -9x + 3y = 12 and 18x - 6y = 20,
[tex]\frac{-9}{18}=\frac{3}{-6}\neq \frac{12}{20}[/tex]
Hence, system −9x + 3y = 12, 18x - 6y = 20 has no solution.
In lines -9x + 3y = 12 and 3x - y = -4,
[tex]\frac{-9}{3}=\frac{3}{-1}= \frac{12}{-4}[/tex]
Hence, system −9x + 3y = 12, 3x - y = -4 has infinitely many solutions.
In lines -9x + 3y = 12 and -16x + 9y = 30 ,
[tex]\frac{-9}{-16}\neq \frac{3}{9}\neq \frac{12}{30}[/tex]
Hence, system −9x + 3y = 12, -16x + 9y = 30 has a solution.
In lines -9x + 3y = 12 and 5x + 8y = -1,
[tex]\frac{-9}{5}\neq \frac{3}{8}\neq \frac{12}{-1}[/tex]
Hence, system −9x + 3y = 12, 5x + 8y = -1 has a solution.
