Verified answer

(i)

3x – y^2 = 1

3x = y^2 + 1

X = (y^2 + 1) / 3

3x – y^2 = 1

-y^2 = 1 – 3x

-1(y^2) = -1(1 – 3x)

Y^2 = 3x – 1

√y^2 = √(3x – 1)

Y = √(3x + 1)

Answers are X = (y^2 + 1) / 3 and Y = √(3x + 1)

(ii)

3x^2 - 3y^2 = 1

3x^2 = 3y^2 + 1

(3x^2)/3 = (3y^2 + 1) / 3

X^2 = y^2 + 1

√x^2 = √(y^2 + 1)

X = √(y^2 + 1)

3x^2 - 3y^2 = 1

-3y^2 = -3x^2 + 1

-3y^2/-3 = -3x^2+1/-3

Y^2 = x^2 + 1

√y^2 = √(x^2 + 1)

Y = √(x^2 + 1)

Answers are X = √(y^2 + 1) and Y = √(x^2 + 1)

(iii)

3x – y = 1

-y = -3x + 1

-y/-1 = (-3x + 1)/-1

Y = 3x – 1

3x – y = 1

3x = y + 1

3x/3 = (y + 1) / 3

X = (y + 1) / 3

Answers are X = (y + 1) / 3 and Y = 3x – 1

(iv)

3x^2 + 3y^2 = 1

3y^2 = -3x^2 + 1

3y^2/3 = (-3x^2 + 1) / 3

y^2 = -x^2 + 1

y^2 = -1(x^2 + 1)

y^2 = x^2 – 1

√y^2 = √(x^2 – 1)

y = √(x^2 – 1)

3x^2 + 3y^2 = 1

3x^2 = -3y^2 + 1

3x^2/3 = (-3y^2 + 1) / 3

X^2 = -y^2 + 1

X^2 = -1(y^2 + 1)

X^2 = y^2 – 1

√x^2 = √(y^2 – 1)

X = √(y^2 – 1)

Answers are X = √(y^2 – 1) and y = √(x^2 – 1)

(v)

3x^2 + 4y^2 = 1

3x^2 = -4y^2 + 1

3x^2 / 3 = (-4y^2 + 1) / 3

X^2 = (-4y^2 + 1) / 3

√x^2 = √((-4y^2 + 1) / 3)

X = √((-4y^2 + 1) / 3)

3x^2 + 4y^2 = 1

4y^2 = -3x^2 + 1

4y^2 / 4 = (-3x^2 + 1) / 4

y^2 = (-3x^2 + 1) / 4

√y^2 = √((-3x^2 + 1) / 4)

y = √((-3x^2 + 1) / 4)

Answers are X = √((-4y^2 + 1) / 3) and y = √((-3x^2 + 1) / 4)