Question

`2x-3y=-16`

`-2x+y=4`
Final Answer: How many solutions are there
1
Infinitly Many Solutions
No Solution

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for the system of equations, we can solve the system and see if there is a unique solution, no solution, or infinitely many solutions.

To solve the system, we can use the method of elimination. We can multiply the second equation by 2 to eliminate the x term:

2*(-2x + y) = 2*4
-4x + 2y = 8

Now the system becomes:
2x - 3y = -16
-4x + 2y = 8

Adding the two equations, we get:
(2x - 3y) + (-4x + 2y) = -16 + 8
-2x - y = -8

Now we have a new equation:
-2x - y = -8

If we compare this with the second equation (-2x + y = 4), we can see that they are actually the same equation (with opposite signs).

Since these two equations are the same, the system has infinitely many solutions.

Therefore, the answer is:
Infinitely Many Solutions