15. solve ( 49x + 9 = 49x + 83 ).\na. does the equation have one solution,\nno solution, or infinitely many…

15. solve ( 49x + 9 = 49x + 83 ).\na. does the equation have one solution,\nno solution, or infinitely many solutions?\nb. write two equations in one variable that\nhave the same number of solutions as this\nequation.

15. solve ( 49x + 9 = 49x + 83 ).\na. does the equation have one solution,\nno solution, or infinitely many solutions?\nb. write two equations in one variable that\nhave the same number of solutions as this\nequation.

Answer

Explanation:

Step1: Subtract (49x) from both sides

$$ \begin{align*} 49x + 9-49x&=49x + 83-49x\ 9&=83 \end{align*} $$ Since (9 = 83) is a false statement.

Step2: Determine the number of solutions

An equation that simplifies to a false statement (like (a=b) where (a\neq b)) has no solution.

For part b, equations like (2x+3=2x + 5) (subtract (2x) gives (3 = 5)) and (5y+1=5y+7) (subtract (5y) gives (1 = 7)) are examples of equations with no solution.

Answer:

a. The equation has no solution. b. Two equations could be (2x + 3=2x+5) and (5y + 1=5y+7)