Answer: No solution.
Explanation:
To solve, we will substitute the first equation into the second equation for the value of y.
Given:
y = 1 - 2x
4x + 2y = 0
Substitute:
4x + 2(1 - 2x) = 0
Distribute:
4x + 2 - 4x = 0
Subtract 2 from both sides of the equation:
4x - 4x = -2
0 = -2
We see that the variables cancel out each other, and now we have nothing to solve or continue moving forward within our solution. This means that there are no solutions to this system of equations.
This means that the lines are parallel. We can also see this when we graph the system, see attached. This becomes more clear when we change both of the equations into slope-intercept form. 4x + 2y = 0 becomes y = -2x, which has the same slope as the first equation (again, parallel lines). If they also had the same y-intercept there would be infinitely many solutions, however, they do not.