Determine the number of solutions to this system of linear equations: 2x+y=6 4x+2y=8
We can solve this system of linear equations by using the second equation to first find the value of x:
4x + 2y = 8
Dividing both sides of the equation by 2:
2x + y = 4
Now, we can use the first equation to substitute the value of y in terms of x:
2x + y = 6
Subtracting 2x from both sides of the equation:
y = 6 - 2x
Now, substitute this value of y in the second equation:
2x + (6 - 2x) = 4
Combine like terms:
(2x - 2x) + 6 = 4
Removing the parentheses:
6 = 4
This equation is not true for any value of x, which means that there are no solutions to this system of linear equations.