Your approach to graph each line by finding the points at which each line intersects the x-axis and y-axis, respectively, was fine. So I suspect the problem may have been in the accuracy of your graph and the scales used. (As you can see from the graph below, the slope of the lines are close, one just a bit steeper than the other.
When estimating the point of intersection using a graph, it always helps to verify, algebraically, the precise point of intersection:
To find the point of intersection: solve the equations simultaneously -
1) $3x-y=4 \iff 6x - 2y = 8 \iff -2y = 8 - 6x$
Now substitute into equation (2):
2) $4x+ -2y=2 \iff 4x + 8 + -6x = 2 \iff -2x = - 6 \iff x = 3$
At $x = 3$, using equation (1), $3\cdot 3 - y = 4 \iff y = 9 - 4 = 5$
Hence the lines intersect at $(3, 5)$.