Certainly! Let's solve the given equations step-by-step to find the values of [tex]\( n \)[/tex] and [tex]\( y \)[/tex].
### Equation (i)
[tex]\[ -7n + 41 = -50 \][/tex]
1. Isolate the term with [tex]\( n \)[/tex]:
Subtract 41 from both sides of the equation to move the constant term to the right side.
[tex]\[ -7n + 41 - 41 = -50 - 41 \][/tex]
[tex]\[ -7n = -91 \][/tex]
2. Solve for [tex]\( n \)[/tex]:
Divide both sides by -7 to isolate [tex]\( n \)[/tex].
[tex]\[ n = \frac{-91}{-7} \][/tex]
[tex]\[ n = 13 \][/tex]
So the solution for [tex]\( n \)[/tex] is:
[tex]\[ n = 13 \][/tex]
### Equation (a)
[tex]\[ \frac{y+4}{-100} = -10 \][/tex]
1. Isolate the term with [tex]\( y \)[/tex]:
Multiply both sides of the equation by -100 to eliminate the denominator.
[tex]\[ (y + 4) \cdot \frac{-100}{-100} = -10 \cdot -100 \][/tex]
[tex]\[ y + 4 = 1000 \][/tex]
2. Solve for [tex]\( y \)[/tex]:
Subtract 4 from both sides to isolate [tex]\( y \)[/tex].
[tex]\[ y + 4 - 4 = 1000 - 4 \][/tex]
[tex]\[ y = 996 \][/tex]
So the solution for [tex]\( y \)[/tex] is:
[tex]\[ y = 996 \][/tex]
### Summary of Solutions:
- For the equation [tex]\( -7n + 41 = -50 \)[/tex], the value of [tex]\( n \)[/tex] is [tex]\( 13 \)[/tex].
- For the equation [tex]\( \frac{y+4}{-100} = -10 \)[/tex], the value of [tex]\( y \)[/tex] is [tex]\( 996 \)[/tex].
Therefore, the solutions to the equations are:
[tex]\[ n = 13, \quad y = 996 \][/tex]
