Chapter 1.1, Problem 2E

To determine

To determine if the below equations are equivalent -

  $-2x=10$ and $-5x=25$

Answer to Problem 2E

The equations are equivalent to each other.

Explanation of Solution

Given: Equations: $-2x=10$ and $-5x=25$

Formula Used:

Equivalent equations are algebraic equations that have identical solutions or roots.

Calculation:

Given :Equations: $-2x=10$ and $-5x=25$

Solving first equation, we have:

  $\begin{array}{l}-2x=10\\ x=-5\end{array}$

Solving second equation, we have:

  $\begin{array}{l}-5x=25\\ x=-5\end{array}$

Both the equations result the same value of $x$ .

From the definition of Equivalent equations and above solutions, both the equations are equivalent to each other,

Conclusion:

Hence, the equations are equivalent to each other.