Solve for x & y and find the value of `9x+3y`:
`2x+5y=13`
`7x-y=27`

Options

A. 39
B. 78
C. 156
D. 312

Answer

To solve the equations \(2x + 5y = 13\) and \(7x - y = 27\), we will use the method of elimination.

### Step 1: Align the equations
We have:
1. \(2x + 5y = 13\) (Equation 1)
2. \(7x - y = 27\) (Equation 2)

### Step 2: Make the coefficients of \(y\) the same
To eliminate \(y\), we can multiply Equation 2 by 5:
\[ 5(7x - y) = 5(27) \]
This gives us:
\[ 35x - 5y = 135 \quad \text{(Equation 3)} \]

### Step 3: Add the equations
Now, we can add Equation 1 and Equation 3:
\[ (2x + 5y) + (35x - 5y) = 13 + 135 \]
This simplifies to:
\[ 2x + 35x + 5y - 5y = 148 \]
\[ 37x = 148 \]

### Step 4: Solve for \(x\)
Now, divide both sides by 37:
\[ x = \frac{148}{37} = 4 \]

### Step 5: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can substitute it back into either original equation to find \(y\). Let's use Equation 2:
\[ 7(4) - y = 27 \]
This simplifies to:
\[ 28 - y = 27 \]
Now, rearranging gives:
\[ y = 28 - 27 = 1 \]

### Step 6: Find the value of \(9x + 3y\)
Now we can find \(9x + 3y\):
\[ 9x + 3y = 9(4) + 3(1) = 36 + 3 = 39 \]

Thus, the solution for \(x\) and \(y\) is:
\[ x = 4, \quad y = 1 \]
And the value of \(9x + 3y\) is:
\[ \boxed{39} \]