Solve the pair of linear equation.
`8x+5y=9, 3x+2y=4`

Answer

To solve the pair of linear equations given by:

1. \( 8x + 5y = 9 \) (Equation 1)
2. \( 3x + 2y = 4 \) (Equation 2)

we will use the elimination method. Here are the steps:

### Step 1: Multiply the equations to align coefficients
To eliminate \(x\), we can multiply Equation 1 by 3 and Equation 2 by 8. This will make the coefficients of \(x\) in both equations equal.

- Multiply Equation 1 by 3:
\[ 3(8x + 5y) = 3(9) \implies 24x + 15y = 27 \quad \text{(Equation 3)} \]

- Multiply Equation 2 by 8:
\[ 8(3x + 2y) = 8(4) \implies 24x + 16y = 32 \quad \text{(Equation 4)} \]

### Step 2: Subtract the new equations
Now, we will subtract Equation 3 from Equation 4 to eliminate \(x\).

\[ (24x + 16y) - (24x + 15y) = 32 - 27 \]

This simplifies to:
\[ 16y - 15y = 5 \implies y = 5 \]

### Step 3: Substitute the value of \(y\) back into one of the original equations
Now that we have \(y\), we can substitute it back into either Equation 1 or Equation 2 to find \(x\). We'll use Equation 2 for simplicity.

Substituting \(y = 5\) into Equation 2:
\[ 3x + 2(5) = 4 \implies 3x + 10 = 4 \]

### Step 4: Solve for \(x\)
Now, isolate \(x\):
\[ 3x = 4 - 10 \implies 3x = -6 \implies x = \frac{-6}{3} = -2 \]

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