system of linear equations

Question

how many solutions does the following system of linear equations have?

4x - 9y = 1

12x - 27y = 3

Answer 1

Note that if you divide the bottom equation by 3, you get the top equation. These are not independent equations, so there are infinitely many (x,y) solutions.

Answer 2

Multiply the terms of the top line by 3 and you have identical lines, therefore INFINITE SOLUTIONS

Answer 3

Hello Lily.

This problem is just like the other one. Multiply every term in the first equation by 3, and you have identical equations of 12x-27y=3. Identical lines intersect at every point, so the answer is INFINITE SOLUTIONS.