Let's start solving the questions step by step based on the given equations:
1. Given the equation [tex]\(2a + 3b = 7\)[/tex], we need to find the value of [tex]\(6a + 9b\)[/tex]:
- To obtain [tex]\(6a + 9b\)[/tex] from [tex]\(2a + 3b\)[/tex], we can multiply the entire equation [tex]\(2a + 3b = 7\)[/tex] by 3.
- This gives us:
[tex]\[
3 \times (2a + 3b) = 3 \times 7
\][/tex]
- Simplifying this, we get:
[tex]\[
6a + 9b = 21
\][/tex]
So, the value of [tex]\(6a + 9b\)[/tex] is [tex]\(21\)[/tex].
2. Now, let's determine the value of [tex]\(3x + 5y\)[/tex] using the given equation [tex]\(6x + 10y = 40\)[/tex]:
- To obtain [tex]\(3x + 5y\)[/tex] from [tex]\(6x + 10y\)[/tex], we can divide the entire equation [tex]\(6x + 10y = 40\)[/tex] by 2.
- This gives us:
[tex]\[
\frac{6x + 10y}{2} = \frac{40}{2}
\][/tex]
- Simplifying this, we get:
[tex]\[
3x + 5y = 20
\][/tex]
So, the value of [tex]\(3x + 5y\)[/tex] is [tex]\(20\)[/tex].
To summarize, the solutions to the given questions are:
(i) The value of [tex]\(6a + 9b\)[/tex] is [tex]\(21\)[/tex].
(ii) The value of [tex]\(3x + 5y\)[/tex] is [tex]\(20\)[/tex].
