I can find no solution to this system of equations.

Solve the system of equations using the substitution method

2x + 4y = -2

2x - y = 4

the 2nd equation says that

y = 2x-4

So, substitute that into the 1st to get

2x + 4(2x-4) = -2

Surely you can solve that, and then find y ...

To solve the system of equations using the substitution method, follow these steps:

Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for x:
2x - y = 4
2x = y + 4
x = (y + 4) / 2

Step 2: Substitute the expression of x from one equation into the other equation.
Substitute the expression of x into the first equation:
2x + 4y = -2
2((y + 4) / 2) + 4y = -2
y + 4 + 4y = -2
5y + 4 = -2
5y = -2 - 4
5y = -6
y = -6 / 5

Step 3: Substitute the value of y back into the equation obtained in Step 1 to solve for x.
x = (y + 4) / 2
x = (-6 / 5 + 4) / 2
x = (-6 + 20) / 10
x = 14 / 10
x = 7 / 5

Therefore, the solution to the system of equations is x = 7/5 and y = -6/5.