Answer: infinitely many solutions
Step 1)
√25y² +16 =5y + 4
(√25y² + 40y + 16)² = (5y + 4)²
25y² + 40y + 16 = (5y + 4)²
25y² + 40y + 16 = (5y)² + 2 × 5y × 4 + 4²
25y² + 40y + 16 = 5² × y² + 2 × 5y × 4 + 4²
25y² + 40y + 16 = 25y² + 2 × 5y × 4 + 16
25y² + 40y + 16 = 25y² + 40y + 16
25y² + 40y + 16 = 25y² + 40y + 16
25y² + 40y + 16 − 25y² − 40y − 16 = 0
0 = 0