Question

how many solutions

y= 5x +7
3y- 15x = 18

Answer 1

[AI-generated answer — Bot GPT 3.5]

There is one unique solution for this system of equations.

By solving the system of equations simultaneously, we find the value of x and y that satisfies both equations.

First, we substitute y = 5x + 7 into the second equation:
3(5x + 7) - 15x = 18
15x + 21 - 15x = 18
21 = 18

This leads to a contradiction, confirming that there is no solution to this system of equations.

Answer 2

what about

x - 2y = 6
3x - 6y = 18

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's solve this system of equations:

1) x - 2y = 6
2) 3x - 6y = 18

We can rewrite equation (1) as x = 2y + 6, and then substitute this into equation (2):

3(2y + 6) - 6y = 18
6y + 18 - 6y = 18
18 = 18

Since the equation simplifies to a true statement, this means that the system of equations is dependent and has infinitely many solutions. This means that the two equations represent the same line and are consistent because they share the same solution set.