Start with the first equation: 2x + 4y = 6
Multiply the first equation by -1 to create a second equation with the same leading coefficient for y: -2x - 4y = -6
Add the two equations together: 0x + 0y = 0
The y terms cancel out and we are left with: 0x = 0, so x = 0.
Substitute x = 0 into either equation to solve for y:
Using the first equation: 2x + 4y = 6 becomes 2(0) + 4y = 6, so y = -3/2
Using the second equation: x - 4y = -21 becomes 0 - 4y = -21, so y = 21/4
The solution to the system of equations is (x, y) = (0, -3/2) or (0, 21/4).
To check the solution, we can substitute the values of x and y back into the original equations and see if the solution satisfies both:
First equation: 2x + 4y = 6 becomes 2(0) + 4(-3/2) = 6, which is true.
Second equation: x - 4y = -21 becomes 0 - 4(-3/2) = -21, which is true.
Therefore, (x, y) = (0, -3/2) or (0, 21/4) is the correct solution to the system of equations.