Solution of the linear equations
3x+2y=4 and 8x+5y=9 is :

Options

A. A)x=2,y=5
B. B)x=-2,y=5
C. C)x=5,y=2
D. D)x=-5,y=-2

Answer

To solve the linear equations \(3x + 2y = 4\) and \(8x + 5y = 9\), we can use the elimination method. Here’s a step-by-step solution:

### Step 1: Write down the equations
We have the following two equations:
1. \(3x + 2y = 4\) (Equation 1)
2. \(8x + 5y = 9\) (Equation 2)

### Step 2: Make the coefficients of \(y\) equal
To eliminate \(y\), we need to make the coefficients of \(y\) in both equations equal. The least common multiple of 2 and 5 is 10.

- Multiply Equation 1 by 5:
\[ 5(3x + 2y) = 5(4) \implies 15x + 10y = 20 \quad \text{(Equation 3)} \]

- Multiply Equation 2 by 2:
\[ 2(8x + 5y) = 2(9) \implies 16x + 10y = 18 \quad \text{(Equation 4)} \]

### Step 3: Subtract the equations
Now, we can subtract Equation 4 from Equation 3 to eliminate \(y\):
\[ (15x + 10y) - (16x + 10y) = 20 - 18 \]
This simplifies to:
\[ 15x - 16x = 2 \implies -x = 2 \]
Thus, we find:
\[ x = -2 \]

### Step 4: Substitute \(x\) back into one of the original equations
Now that we have \(x\), we can substitute it back into one of the original equations to find \(y\). We will use Equation 1:
\[ 3(-2) + 2y = 4 \]
This simplifies to:
\[ -6 + 2y = 4 \]
Adding 6 to both sides gives:
\[ 2y = 10 \]
Dividing by 2, we find:
\[ y = 5 \]

### Final Solution
The solution to the system of equations is:
\[ x = -2, \quad y = 5 \]

### Summary
Thus, the solution of the linear equations \(3x + 2y = 4\) and \(8x + 5y = 9\) is:
\[ (x, y) = (-2, 5) \]