Question

Error AnalysisDescribe and correct the error in solving the equation.6(2y+6)=4(9+3y)12y+36=36+12y12y=12y0=0The equation has no solution

Answer 1

Given:

`6(2y+6)=4(9+3y)`

Simplifying the equation further,

`\begin{gathered} 12y+36=36+12y \\ Subtracting\text{ 36 from both sides;} \\ 12y+36-36=36-36+12y \\ 12y=12y \\ Dividing\text{ both sides by 12;} \\ (12y)/(12)=(12y)/(12) \\ y=y \end{gathered}`

Both equations are equal. When two equations are equal, the system will have infinitely many solutions.

From the above, the equation has infinitely many solutions.