Question

Determine the value of the variable in the simplified expressions.

What is the value of x?


gx + h−3 =
1
g6
+
1
h3

x =


What is the value of y?

b4c−7 =
by
c7

y =

Answer 1

To find the values of \( x \) and \( y \), we need to simplify the given equations step by step.

### For the first equation:

1. **Equation Given**:
\[
gx + h - 3 = \frac{1}{g6} + \frac{1}{h3}
\]

2. **Simplifying**:
The right-hand side can be simplified, but let's first rewrite the equation. Since \( g6 \) and \( h3 \) may represent constants (let's assume \( g \) and \( h \) are not equal to zero), we can rewrite it without substitutions for now.

3. **Finding \( x \)**:
Try to isolate \( x \):
\[
gx = \frac{1}{g6} + \frac{1}{h3} - h + 3
\]
To make it simpler and assuming \( g \) and \( h \) are known constants, you will typically substitute values for \( g \) and \( h \) to find \( x \).

### Without specific values for \( g \) and \( h \), we can't find a numeric answer.

### For the second equation:

1. **Equation Given**:
\[
b4c - 7 = byc^7
\]

2. **Changing the equation**:
Rearrange the equation:
\[
b4c - byc^7 = 7
\]

3. **Factoring out the common terms**:
Let's factor out common variables:
\[
b(4c - yc^7) = 7
\]
Assuming \( b \) is a constant not equal to zero, we can divide through by \( b \):
\[
4c - yc^7 = \frac{7}{b}
\]

4. **Finding \( y \)**:
Rearranging gives:
\[
yc^7 = 4c - \frac{7}{b}
\]
Then:
\[
y = \frac{4c - \frac{7}{b}}{c^7}
\]

### Again, without specific values for \( b \) and \( c \), we can't find a numeric answer.

### Conclusion:
- To find the values of \( x \) and \( y \), you need the values of \( g, h, b, \) and \( c \) to provide specific numerical results.
- If you have further details or specific values for \( g, h, b, \) and \( c \), please provide them for further assistance!