Determine the number of solutions to this system of linear equations: 2x+y=6 4x+2y=8 (1 point) Responses 1 1 2 2 infinite infinite 0
The given system of linear equations is:
2x + y = 6 ---> Equation (1)
4x + 2y = 8 ---> Equation (2)
To determine the number of solutions, we can rewrite Equation (2) by dividing every term by 2:
2x + y = 4 ---> Equation (3)
We can see that Equations (1) and (3) have the same equation when multiplied by 2. This means that the two equations represent the same line.
Therefore, the system of equations has infinite solutions.
Hence, the correct response is: infinite