Find the x- and y-intercepts (if any) for each line. Show your work. Plot those

Question

Find the x- and y-intercepts (if any) for each line. Show your work.
Plot those intercepts, and graph the two lines on the same chart. Submit your graph through the Dropbox.
Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.
The 2 equations are:
x + 5y = 29
-7x + 4y = 70
Below is what I came up with but I just want to know if I did this correctly.
x + 5y = 29
y = 0 x + 5(0) = 29
x = 29
x = 0 0 + 5y = 29
5y = 29
y = 29/5
-7x + 4y = 70
y = 0 -7x + 4(0)= 70
-7x = 70
x = -10
x = 0 -7(0) + 4y = 70
4y = 70
y = 70/4 = 35/2

I will use the substitution system to point of intersection.
x = 29 - 5y
-7(29 - 5y) + 4y = 70
-203 + 35y + 4y = 70
39y = 273
y = 7
x + 5(7) = 29
x + 35 = 29
x = 29/35

Explanation / Answer

x + 35 = 29
x = 29/35
Very good except the last statement should be:
x = 29 - 35 = -6

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