Certainly! Let's solve these equations step-by-step to find the value of [tex]\( b \)[/tex].
1. First Equation:
[tex]\[
\frac{5a - 3}{9} = 3
\][/tex]
- Start by isolating [tex]\( 5a - 3 \)[/tex]:
[tex]\[
5a - 3 = 3 \times 9
\][/tex]
Simplify on the right-hand side:
[tex]\[
5a - 3 = 27
\][/tex]
- Solve for [tex]\( a \)[/tex]:
[tex]\[
5a = 27 + 3
\][/tex]
[tex]\[
5a = 30
\][/tex]
[tex]\[
a = \frac{30}{5}
\][/tex]
[tex]\[
a = 6
\][/tex]
Now we have [tex]\( a = 6 \)[/tex].
2. Second Equation:
[tex]\[
7b - 1 = a - 21
\][/tex]
Substitute [tex]\( a = 6 \)[/tex] into the second equation:
[tex]\[
7b - 1 = 6 - 21
\][/tex]
Simplify the right-hand side:
[tex]\[
7b - 1 = -15
\][/tex]
- Solve for [tex]\( b \)[/tex]:
[tex]\[
7b = -15 + 1
\][/tex]
[tex]\[
7b = -14
\][/tex]
[tex]\[
b = \frac{-14}{7}
\][/tex]
[tex]\[
b = -2
\][/tex]
Therefore, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are:
[tex]\[
a = 6 \quad \text{and} \quad b = -2
\][/tex]
