Question

Determine the number of solutions to this system of linear equations: 2x+y=6 4x+2y=8 (1 point)

1 2 infinite 0

Answer 1

[AI-generated answer — Explain Bot]

To determine the number of solutions to the given system of linear equations, we can use several methods such as graphing, substitution, or elimination.

Here, let's use the elimination method to solve the system of equations:

Given equations:
1) 2x + y = 6
2) 4x + 2y = 8

We can start by multiplying equation 1 by -2, which will allow us to eliminate the variable "y" when we add the equations together:

-2 * (2x + y) = -2 * 6
-4x - 2y = -12

Now, we can add the two equations together:

-4x - 2y + 4x + 2y = -12 + 8
0 = -4

When the equation simplifies to 0 = -4, we have a contradiction. This means that the system of equations does not have a solution. Therefore, the correct option is 0 (zero) solutions.

To summarize, the system of linear equations 2x + y = 6 and 4x + 2y = 8 does not have any solutions.