If 3x+5y=44 and 10x-2y=16 what is the value of x?

Options

A. 7
B. 3
C. 5.5
D. 6.5

Answer

To solve the system of equations given by \(3x + 5y = 44\) and \(10x - 2y = 16\), we can follow these steps:

### Step 1: Write down the equations
We have:
1. \(3x + 5y = 44\) (Equation 1)
2. \(10x - 2y = 16\) (Equation 2)

### Step 2: Multiply the first equation by 2
To eliminate \(y\), we can make the coefficients of \(y\) in both equations equal. We will multiply Equation 1 by 2:
\[ 2(3x + 5y) = 2(44) \]
This simplifies to:
\[ 6x + 10y = 88 \quad \text{(Equation 3)} \]

### Step 3: Multiply the second equation by 5
Next, we multiply Equation 2 by 5:
\[ 5(10x - 2y) = 5(16) \]
This simplifies to:
\[ 50x - 10y = 80 \quad \text{(Equation 4)} \]

### Step 4: Add Equation 3 and Equation 4
Now, we will add Equation 3 and Equation 4:
\[ (6x + 10y) + (50x - 10y) = 88 + 80 \]
This simplifies to:
\[ 56x + 0y = 168 \]

### Step 5: Solve for \(x\)
Now, we can solve for \(x\):
\[ 56x = 168 \]
Dividing both sides by 56 gives:
\[ x = \frac{168}{56} = 3 \]

### Final Answer
Thus, the value of \(x\) is \(3\).

---