Question

Which system of equations has infinitely many solutions? A. 3y = –5x + 7 3x = –5y – 7 B. 3y = x – 4 3x – 9y = –12 C. 2x + y = 2 –4x – 2y = 4 D. 2y = 3x + 6 4y = 6x + 12

Answer 1

Option B) has infintely many solutions

That is Option B) 3y=x-4 and 3x-9y=-12 has infintely many solutions

Explanation:

A system will have infinitely many solutions if each equations refers to the same line.

Given equations are

3y=x-4 and 3x-9y=-12 both the lines represents same line equation.In the given equations we have equations end up with unequal values on each side of the equation.

That is 3y=x-4

x-3y=4

Multiply with 3 we get

3x-9y=12

comparing the equations 3x-9y=12 and 3x-9y=-12 we get that the given system of equations has infinite solutions

Therefore option B) has infintely many solutions