Chapter 1.1, Problem 2E

To determine

To show: That the equation $-2x=10$ and $-5x=25$ are equivalent. equivalent.

Explanation of Solution

Given information:

Two equations $-2x=10$ and $-5x=25$ .

Formula used:

Definition: - Two linear systems is equivalent if and only if they have the same solution set.

Calculation:

Now simplify the equation $-2x=10$

Divide both sides by $-2$ and further simplify it

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

Now simplify the equation $-5x=25$

Divide both sides by $-5$ and further simplify it

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

Since, both the equation has same solution.

Therefore, the equation $-2x=10$ and equation $-5x=25$ are equivalent.

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