Determine the number of solutions to this system of linear equations:
2x+y=6
4x+2y=8 (1 point)
Responses
0
0
1
1
infinite
infinite
2
1
To determine the number of solutions to the system of linear equations, we can use the method of elimination or substitution to simplify the equations and see if there is a unique solution, no solution, or infinitely many solutions.
Let's use the elimination method to solve the given system of equations:
1) Multiply the first equation by -2 to make the coefficients of x in both equations equal: -4x - 2y = -12.
2) Now, we have the system of equations:
-4x - 2y = -12
4x + 2y = 8
When we add the two equations together, we get:
0 = -4
This equation implies that 0 is not equal to -4 and thus has no solution. Therefore, the number of solutions to the given system of linear equations is 0.
So, the answer is:
0