Question

How many solutions does the system of equations have?

6x+2y=−18
3x+y=24(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The system of equations has one solution.

Answer 2

[AI-generated answer — Explain Bot]

To determine how many solutions the system of equations has, we can use the method of elimination or substitution. Let's use the method of elimination:

1. Multiply the second equation by 2 to make the coefficients of y's in both equations equal:
- Original: 6x + 2y = -18
- Multiply the second equation by 2: 6x + 2y = 48

2. Now, subtract the original first equation from the modified second equation:
(6x + 2y) - (6x + 2y) = 48 - (-18)
0 = 66

When we solve this equation, we find that 0 equals a non-zero number (66). This contradiction means that there is no solution to the system of equations.

Therefore, the system of equations has no solution.