Let's solve each of the equations step by step.
Equation 1
\[ (7y - 90) \cdot \frac{16}{8} = \frac{24}{12} \]
Simplifying both sides: \[ (7y - 90) \cdot 2 = 2 \] \[ 7y - 90 = 1 \] \[ 7y = 91 \] \[ y = \frac{91}{7} = 13 \]
Equation 2
\[ \frac{(12x - 35)}{11} : 5 = \frac{42}{6} \]
Simplifying the right side: \[ \frac{(12x - 35)}{11} \cdot \frac{1}{5} = 7 \quad \Rightarrow \quad (12x - 35) = 7 \cdot 55 \] \[ (12x - 35) = 385 \] \[ 12x = 420 \] \[ x = \frac{420}{12} = 35 \]
Equation 3
\[ 12x + 2x = 54 + 8 \cdot 2 \] \[ 14x = 54 + 16 \] \[ 14x = 70 \] \[ x = \frac{70}{14} = 5 \]
Equation 4
\[ 5x + 4x = 41 + 8 \cdot 5 \] \[ 9x = 41 + 40 \] \[ 9x = 81 \] \[ x = \frac{81}{9} = 9 \]
Equation 5
\[ 11x - 9x - 13 = 59 \] \[ 2x - 13 = 59 \] \[ 2x = 72 \] \[ x = \frac{72}{2} = 36 \]
Summary of Solutions
- \( y = 13 \)
- \( x = 35 \)
- \( x = 5 \) (this is a different value of \( x \) than the previous equations)
- \( x = 9 \) (yet another value of \( x \))
- \( x = 36 \)
Please verify whether you're solving for all instances of \( x \) and \( y \) throughout your concerns. The equations yield multiple values for \( x \).