To solve for [tex]\( y \)[/tex] given the equation [tex]\( v \cdot (j + y) = 61y + 82 \)[/tex], follow these steps:
1. Distribute [tex]\( v \)[/tex] on the left-hand side:
[tex]\[ v \cdot j + v \cdot y = 61y + 82 \][/tex]
2. Rearrange the equation to isolate terms involving [tex]\( y \)[/tex]:
[tex]\[ vj + vy = 61y + 82 \][/tex]
3. Move all [tex]\( y \)[/tex]-terms to one side of the equation:
[tex]\[ vy - 61y = 82 - vj \][/tex]
4. Factor out [tex]\( y \)[/tex] from the left-hand side:
[tex]\[ y(v - 61) = 82 - vj \][/tex]
5. Solve for [tex]\( y \)[/tex] by dividing both sides of the equation by [tex]\( (v - 61) \)[/tex]:
[tex]\[ y = \frac{82 - vj}{v - 61} \][/tex]
So, the solution for [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{82 - vj}{v - 61} \][/tex]
Hence:
[tex]\[ \boxed{ \frac{82 - vj}{v - 61} } \][/tex]
