Question 287295
I suspect that  you forgot to include y in the second equation
I will place it where I think it should be.
10x+y=4
30x-12y=-3
The slope of the first is -10/1=-10
The slope of the second is -30/-12=15/6=5/2=2.5
So they are not parallel and not perpendicular
multiply the first by -3
-30x-3y=-12
30x-12y=-3
add them
-15y=-15
y=1
10x+1=4
10x=3
x=3/10
The only solution is (3/10,1)
Google "independent consistent"