If `2x+1=8 and 15-3y=0,` what is the value of `(x)/(y)`?

Answer

To solve the equations \(2x + 1 = 8\) and \(15 - 3y = 0\) and find the value of \(\frac{x}{y}\), we will follow these steps:

### Step 1: Solve for \(x\)
We start with the equation:
\[ 2x + 1 = 8 \]
Subtract 1 from both sides:
\[ 2x = 8 - 1 \]
\[ 2x = 7 \]
Now, divide both sides by 2:
\[ x = \frac{7}{2} \]

### Step 2: Solve for \(y\)
Next, we solve the equation:
\[ 15 - 3y = 0 \]
Add \(3y\) to both sides:
\[ 15 = 3y \]
Now, divide both sides by 3:
\[ y = \frac{15}{3} \]
\[ y = 5 \]

### Step 3: Calculate \(\frac{x}{y}\)
Now that we have the values of \(x\) and \(y\):
\[ x = \frac{7}{2}, \quad y = 5 \]
We can find \(\frac{x}{y}\):
\[ \frac{x}{y} = \frac{\frac{7}{2}}{5} \]
This can be simplified by multiplying the numerator by the reciprocal of the denominator:
\[ \frac{x}{y} = \frac{7}{2} \times \frac{1}{5} = \frac{7}{10} \]

### Final Answer
Thus, the value of \(\frac{x}{y}\) is:
\[ \frac{x}{y} = \frac{7}{10} \]

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