The value of x and y in the equations `5x+2y=16 and 7x-4y=2` are :

Options

A. `x=2, y=3`
B. `x=3,y=2`
C. `x=1, y=2`
D. None of these

Answer

To solve the equations \(5x + 2y = 16\) and \(7x - 4y = 2\), we can use the method of elimination. Here’s a step-by-step solution:

### Step 1: Write down the equations
We have:
1. \(5x + 2y = 16\) (Equation 1)
2. \(7x - 4y = 2\) (Equation 2)

### Step 2: Make the coefficients of \(y\) the same
To eliminate \(y\), we can multiply Equation 1 by 2 to make the coefficient of \(y\) in both equations the same:
\[ 2(5x + 2y) = 2(16) \]
This simplifies to:
\[ 10x + 4y = 32 \quad \text{(Equation 3)} \]

### Step 3: Add the modified Equation 3 to Equation 2
Now we can add Equation 3 and Equation 2:
\[ (10x + 4y) + (7x - 4y) = 32 + 2 \]
This simplifies to:
\[ 10x + 7x + 4y - 4y = 34 \]
\[ 17x = 34 \]

### Step 4: Solve for \(x\)
Now, divide both sides by 17:
\[ x = \frac{34}{17} = 2 \]

### Step 5: Substitute \(x\) back into one of the original equations
Now that we have \(x\), we can substitute \(x = 2\) back into Equation 1 to find \(y\):
\[ 5(2) + 2y = 16 \]
This simplifies to:
\[ 10 + 2y = 16 \]
Subtract 10 from both sides:
\[ 2y = 6 \]
Now, divide by 2:
\[ y = \frac{6}{2} = 3 \]

### Final Answer
Thus, the values of \(x\) and \(y\) are:
\[ x = 2, \quad y = 3 \]

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