Question

Q25 Determine whether the following equations have the same solution set.
4y - 9 = 3y + 15
5y + 20 = 35
2b - 4b + 6b = 12

Answer 1

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

1. **For the first equation:**
\[
4y - 9 = 3y + 15
\]
Start by isolating \(y\):
\[
4y - 3y = 15 + 9
\]
Simplifying gives:
\[
y = 24
\]

2. **For the second equation:**
\[
5y + 20 = 35
\]
First, isolate \(y\):
\[
5y = 35 - 20
\]
Which simplifies to:
\[
5y = 15
\]
Dividing both sides by 5 gives:
\[
y = 3
\]

3. **For the third equation:**
\[
2b - 4b + 6b = 12
\]
Combine like terms:
\[
(2 - 4 + 6)b = 12
\]
Simplifying the coefficients:
\[
4b = 12
\]
Dividing both sides by 4 results in:
\[
b = 3
\]

**Summary of solutions:**
- From the first equation, we found \(y = 24\).
- From the second equation, we found \(y = 3\).
- From the third equation, we also found \(b = 3\).

**Conclusion:**
The first equation has the solution \(y = 24\), while the second and third equations both have the solution \(y = 3\) (or \(b = 3\)). Therefore, the given equations do not have the same solution set.