Answer
equivalent equations
Work Step by Step
$\bf{\text{Solution Outline:}}$
Solve the solution sets of the given statements,
\begin{array}{l}\require{cancel}
\dfrac{3}{5}a+\dfrac{1}{5}=2
\\\text{and}\\
3a+1=10
.\end{array}
If the solution sets are the same, then they are equivalent. Otherwise, they are not equivalent.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the first equation is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3}{5}a+\dfrac{1}{5}=2
\\\\
5\left( \dfrac{3}{5}a+\dfrac{1}{5} \right)=5(2)
\\\\
3a+1=10
.\end{array}
Since the equation above is the same as the second given equation, then the given are $\text{
equivalent equations
.}$
