This is what you call systems of equations. Basically were the two equations cross on a graph is the solution
You can solve this multiply ways... Graph, table, Substitution, elimination...
I will choose elimination because it is the easiest for how the equations are set up.
So
4x+2y = 200 2x+7y=400
First I take the second equation and multiply it by 2..
2(2x) + 2(7y)= 2(400)
4x+14y=800
Now I can just subtract the two equations
4x+2y = 200
-(4x+14y=800)
____________
-12y=-600
Solve for y
-12y/-12=-600/-12
y=50
Plug back in
4x+2y = 200
4x+2(50)=200
4x+100=200
-100 - 100
4x=100
4x/4=100/4
x=25
(25,50)
To check if you are correct you can use something like desmos (online graphing tool) and see if (25,50) is were the two lines cross.
You can also use substitution if you prefer.