Given the transformation (x,y)→(x, 2x + y) determine the equation of the line 3x + 5y -30 = 0 after it undergoes this transformation.?

Answer 1

(x, y) → (X, 2X + Y)

3x + 5y - 30 = 0

3(X) + 5 (2X + Y) - 30 = 0

3X + 10X+ 5Y - 30 = 0

13X + 5Y - 30 = 0

Now transferred equation 13X + 5Y - 30 = 0

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Answer 2

x' = x

y'=2x+y=2x'+y --->y=y'-2x'

replace x,y into 3x + 5y -30 = 0 ---> 3x'+5(y'-2x')-30=0 or -7x'+5y'-30=0

or

7x-5y+30=0

Answer 3

That line is y = 6 – (3/5)x

A point on that line is therefore [x, 6 – (3/5)x]

In the transformation x →x, but,

y→ (2x + y) = 2x + 6 – (3/5)x = (7/5)x + 6

A point on the new line is therefore [x, (7/5)x + 6]

The equation of the new line is y = (7/5)x + 6, or,

5y – 7x – 30 = 0