Determine the number of solutions to this system of linear equations:. 2x+y=6. 4x+2y=8
This system of linear equations represents two equations in two variables:
1) 2x + y = 6
2) 4x + 2y = 8
To determine the number of solutions, we need to analyze the coefficients of the variables.
If the coefficients of the variables are not proportional, the system has a unique solution, meaning there is only one solution that satisfies both equations.
If the coefficients of the variables are proportional, the system has infinitely many solutions, meaning there are an infinite number of solutions that satisfy both equations.
Let's analyze the coefficients:
1) The coefficient of x in equation 1 is 2, and in equation 2 is also 2. These coefficients are proportional.
2) The coefficient of y in equation 1 is 1, and in equation 2 is 2. These coefficients are not proportional.
Since the coefficients of x are proportional but the coefficients of y are not proportional, this system of linear equations has infinitely many solutions.