To determine the values of \( x \) and \( y \) in the simplified expressions you provided, we will solve each equation step-by-step.
1. Solve for \( x \):
You provided the equation: \[ gx + h - 3 = 1g6 + 1h3 \]
Assuming \( 1g6 \) represents \( g \cdot 6 \) and \( 1h3 \) represents \( h \cdot 3 \), the equation can be rewritten as: \[ gx + h - 3 = 6g + 3h \]
Next, to isolate the term involving \( x \), we subtract \( h \) from both sides: \[ gx - 3 = 6g + 3h - h \] \[ gx - 3 = 6g + 2h \]
Now, we add \( 3 \) to both sides: \[ gx = 6g + 2h + 3 \]
Finally, divide both sides by \( g \): \[ x = \frac{6g + 2h + 3}{g} \]
Thus: \[ x = 6 + \frac{2h}{g} + \frac{3}{g} \]
2. Solve for \( y \):
You provided the equation: \[ b4c - 7 = byc7 \]
Assuming \( b4c \) represents \( b \cdot 4 \cdot c \) and \( byc7 \) represents \( b \cdot y \cdot c \cdot 7 \): \[ b \cdot 4 \cdot c - 7 = b \cdot y \cdot c \cdot 7 \]
To isolate \( y \), we first add \( 7 \) to both sides: \[ b \cdot 4 \cdot c = b \cdot y \cdot c \cdot 7 + 7 \]
Now, we can factor out \( b \cdot c \) from the left side: \[ 4bc = 7byc + 7 \]
Next, we can factor out \( b \) from the right-side: \[ 4bc = byc \cdot 7 + 7 \]
To isolate \( y \), we can move \( 7ybc \) to the other side: \[ 4bc - 7 = 7byc \]
Now, divide through by \( 7bc \): \[ y = \frac{4c - 7}{7c} \]
So, the solution for \( y \) can be simplified further if needed: \[ y = \frac{4}{7} - \frac{1}{b} \]
Conclusion:
- The value of \( x = 6 + \frac{2h}{g} + \frac{3}{g} \)
- The value of \( y = \frac{4c - 7}{7c} \)
Please verify if my interpretation of the variable expressions is correct, and if any specific variables or relationships were intended but not explicitly stated, feel free to clarify!