y=-2x+5

2y+4x=10
solve the system ?

The two equations are not independent. The first equation can be written

2y = -4x +10
or
2x + 4x = 10
which is the same as the second equation.

There is therefore no unique (x,y) solution. There are an infinite number of solutions.

To solve the system of equations, we'll use the substitution method. Let's begin:

1) Start with the equation y = -2x + 5.

2) Substitute this expression for y in the second equation:
2(-2x + 5) + 4x = 10.

3) Distribute the 2:
-4x + 10 + 4x = 10.

4) Combine like terms:
10 = 10.

5) This equation is true, which indicates that the system of equations is dependent or consistent. This means the two equations represent the same line, and hence there are infinite solutions.

In conclusion, the system of equations is dependent, with infinitely many solutions.