Solve the following system using the substitution method 2y +5x = 10 4y + 10x = 2

The given system of equations has no solution 

Explanation:
The first given equation is:
2y + 5x = 10
This can be rewritten as:
2y = 10 - 5x ...............> equation I
The second given equation is:
4y + 10x = 2
This can be rewritten as:
2(2y) + 10x = 2 ................> equation II

Substitute with I in II and solve as follows:
2(2y) + 10x = 2
2(10-5x) + 10x = 2
20 - 10x + 10x = 2
20 = 2
Since this is impossible, therefore, the system of equations has no solutions. This means that there is no (x,y) point that would satisfy both equations.

Graphing check:
The attached image shows the graphs of the two given functions. We can note that the two lines are parallel each with slope -5/2, which means that they NEVER intersect. 
Hence, there is no solution for the given system.

Hope this helps :)