Question

Does the following equations have the same solution set 7z + 5 = 2z + 30 3D - 10 = 5 c minus 5c + 9 c = 27

Answer 1

To determine if the equations have the same solution set, we will solve each equation step by step.

**1. Solve the first equation:**
\[
7z + 5 = 2z + 30
\]

Subtract \(2z\) from both sides:
\[
7z - 2z + 5 = 30
\]

This simplifies to:
\[
5z + 5 = 30
\]

Next, subtract 5 from both sides:
\[
5z = 25
\]

Now, divide both sides by 5:
\[
z = 5
\]

**2. Solve the second equation:**
\[
3D - 10 = 5c - 5c + 9c = 27
\]

First, simplify \(5c - 5c + 9c\) to just \(9c\):
\[
3D - 10 + 9c = 27
\]

Now, isolate \(3D\):
\[
3D = 27 + 10 - 9c
\]
\[
3D = 37 - 9c
\]

Now, solving for \(D\):
\[
D = \frac{37 - 9c}{3}
\]

**Conclusion:**

The first equation yields a single solution \(z = 5\), while the second equation provides a solution for \(D\) in terms of \(c\), and does not provide a unique solution set. Since the first equation has a specific solution for \(z\) and the second represents a relationship between \(D\) and \(c\) without tying it down to a specific value, these equations do not have the same solution set.

Thus, the answer is **No**, the equations do not have the same solution set.