Solve the equation. Check each solution.

Question

(y/2)+(y/7)=9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
1)The solution is y=____ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
2) There are infinitely many solutions.
3)There is no solution.

Answer 1

To solve the equation \((y/2) + (y/7) = 9\), we first need to find a common denominator for the fractions on the left side.

The common denominator of 2 and 7 is 14. Thus, we can rewrite the equation as:

\[ \frac{7y}{14} + \frac{2y}{14} = 9 \]

Now, combine the fractions:

\[ \frac{7y + 2y}{14} = 9 \]

This simplifies to:

\[ \frac{9y}{14} = 9 \]

Next, we can eliminate the fraction by multiplying both sides by 14:

\[ 9y = 9 \cdot 14 \]

Calculating the right side gives:

\[ 9y = 126 \]

Now, divide both sides by 9:

\[ y = \frac{126}{9} \]

Simplifying \(\frac{126}{9}\):

\[ y = \frac{14}{1} = 14 \]

So, the solution is:

1. The solution is \( y = 14 \).

To check the solution, substitute \(y = 14\) back into the original equation:

\[ \frac{14}{2} + \frac{14}{7} = 9 \] \[ 7 + 2 = 9 \]

The left side equals the right side, confirming that our solution is correct.

Thus, the final answer is:

1. The solution is \( y = 14 \).