The way you worded the question, it appears that you want equation solved for each variable. However, I am wondering if you what you are really looking for are the x and y intercepts. I will do both, just to make sure you get the answer you need.
solve for x
2y + 32x = 34
32x = 34 - 2y subtract 2y from both sides
x = [tex] \frac{34}{32} [/tex] - [tex] \frac{2y}{32} [/tex] divided both sides by 32
x = [tex] \frac{17}{16} [/tex] - [tex] \frac{y}{16} [/tex] simplified the fractions
solve for y
2y + 32x = 34
2y = 34 - 32x subtract 32x from both sides
y = [tex] \frac{34}{2} [/tex] - [tex] \frac{32x}{2} [/tex] divided both sides by 2
y = 17 - 16x simplified the fractions
x-intercept - when y=0
2(0) + 32x = 34
32x = 34
x = [tex] \frac{34}{32} [/tex] = [tex] \frac{17}{16} [/tex]
y-intercept - when x=0
2y + 32(0) = 34
2y = 34
y = [tex] \frac{34}{2} [/tex] = 17
