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You have not said what it is that "solve" means in this case. There are a number of possibilities. (These are just a few to give you the idea. There are many more possibilities.)
Solve for y
2+3y = 5x
3y = 5x - 2 (subtract 2 from both sides)
y = (5/3)x - (2/3) (divide both sides by 3)
Solve for x
5x = 3y + 2 (rearrange)
x = (3/5)y + 2/5 (divide both sides by 5)
Find the y-intercept
2 + 3y = 5(0) (set x=0)
3y = -2 (subtract 2 from both sides)
y = -2/3 (divide both sides by 3. Note, we did this in "Solve for y" above.)
y-intercept is (0, -2/3)
Find the x-intercept
2 + 3(0) = 5x (set y=0)
2/5 = x (divide both sides by 5. Note, we did this in "Solve for x" above.)
x-intercept is (2/5, 0)
Put in standard form
2 + 3y = 5x
5x - 3y = 2 (subtract 3y from both sides; swap sides)
Solve for y
2+3y = 5x
3y = 5x - 2 (subtract 2 from both sides)
y = (5/3)x - (2/3) (divide both sides by 3)
Solve for x
5x = 3y + 2 (rearrange)
x = (3/5)y + 2/5 (divide both sides by 5)
Find the y-intercept
2 + 3y = 5(0) (set x=0)
3y = -2 (subtract 2 from both sides)
y = -2/3 (divide both sides by 3. Note, we did this in "Solve for y" above.)
y-intercept is (0, -2/3)
Find the x-intercept
2 + 3(0) = 5x (set y=0)
2/5 = x (divide both sides by 5. Note, we did this in "Solve for x" above.)
x-intercept is (2/5, 0)
Put in standard form
2 + 3y = 5x
5x - 3y = 2 (subtract 3y from both sides; swap sides)
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