Alright, let’s solve for the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] using the given equations.
### Step 1: Solve the first equation for [tex]\(a\)[/tex]
The first equation is:
[tex]\[ \frac{5a - 3}{9} = 3 \][/tex]
To solve for [tex]\(a\)[/tex], follow these steps:
1. Multiply both sides by 9 to eliminate the fraction:
[tex]\[ 5a - 3 = 27 \][/tex]
2. Add 3 to both sides to isolate the term with [tex]\(a\)[/tex]:
[tex]\[ 5a = 30 \][/tex]
3. Divide both sides by 5 to solve for [tex]\(a\)[/tex]:
[tex]\[ a = 6 \][/tex]
### Step 2: Substitute [tex]\(a = 6\)[/tex] into the second equation
The second equation is:
[tex]\[ 7b - 1 = a - 21 \][/tex]
Substitute [tex]\(a = 6\)[/tex] into the equation:
[tex]\[ 7b - 1 = 6 - 21 \][/tex]
Simplify the right-hand side:
[tex]\[ 7b - 1 = -15 \][/tex]
### Step 3: Solve for [tex]\(b\)[/tex]
To solve for [tex]\(b\)[/tex], follow these steps:
1. Add 1 to both sides to isolate the term with [tex]\(b\)[/tex]:
[tex]\[ 7b = -14 \][/tex]
2. Divide both sides by 7:
[tex]\[ b = -2 \][/tex]
### Conclusion
The solutions to the given equations are:
[tex]\[ a = 6 \][/tex]
[tex]\[ b = -2 \][/tex]
