Question

question 15 (1 point) solve the equation. -2y + 5 + y² = -6y + 2y² a y = -1 and y = 5 b y = -5 c y = -5 and y = 1 d no real solution

Explanation:

Step1: Rearrange the equation

Move all terms to one side: \(y^{2}-2y + 5+6y - 2y^{2}=0\)
Simplify: \(-y^{2}+4y + 5 = 0\)
Multiply by -1: \(y^{2}-4y - 5 = 0\)

Step2: Factor the quadratic

Find two numbers that multiply to -5 and add to -4: -5 and 1.
So, \(y^{2}-4y - 5=(y - 5)(y + 1)=0\)

Step3: Solve for y

Set each factor to zero:
\(y - 5 = 0\) gives \(y = 5\)
\(y + 1 = 0\) gives \(y=-1\)

Answer:

a. \(y = -1\) and \(y = 5\)