Look at these equations. Use both equations to work out the value of [tex][tex]$b$[/tex][/tex].

[tex]\[
\begin{array}{l}
\frac{5a-3}{9}=3 \\
7b-1=a-21
\end{array}
\][/tex]



Answer :

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]