Respuesta :
the equations y = –3x + 4 and 3y = –9x + 12 have infinitely many solutions. option B is correct.
What is the linear system?
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Condition for the parallel lines.
L1, ax + bx + c = 0
L2, dx + ey + f = 0
If [tex]\rm \dfrac{a}{d} = \dfrac{b}{e} = \dfrac{c}{f}[/tex] then lines have infinitely many solutions.
Which system of equations below has infinitely many solutions?
y = –3x + 4 and 3y = –9x + 12
On comparing we have
a = -3 , b = 1, and c = 4
d = -9 , e = 3, and f = 12
Then their ratio will be
[tex]\rm \dfrac{1}{3} = \dfrac{-3}{-9} = \dfrac{4}{12}\\\\\rm \dfrac{1}{3} = \dfrac{1}{3} = \dfrac{1}{3}[/tex]
Hence y = –3x + 4 and 3y = –9x + 12 have infinitely many solutions.
Thus the option B is correct.
More about the linear system link is given below.
https://brainly.com/question/20379472
