Question

Which system of equations below has infinitely many solutions? y = –3x 4 and y = –3x – 4 y = –3x 4 and 3y = –9x 12 y = –3x 4 and y = Negative one-thirdx 4 y = –3x 4 and y = –6x 8.

Answer 1

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 $\rm \dfrac{a}{d} = \dfrac{b}{e} = \dfrac{c}{f}$ 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

$\rm \dfrac{1}{3} = \dfrac{-3}{-9} = \dfrac{4}{12}\\\\\rm \dfrac{1}{3} = \dfrac{1}{3} = \dfrac{1}{3}$

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.

brainly.com/question/20379472