Solve the following pair of linear equations by substitution methods.
`8x+5y=9`.
`3x+2y=4.`

Answer

To solve the pair of linear equations using the substitution method, we will follow these steps:

### Step 1: Solve one equation for one variable
We start with the first equation:
\[ 8x + 5y = 9 \]
We can express \( x \) in terms of \( y \):
\[ 8x = 9 - 5y \]
\[ x = \frac{9 - 5y}{8} \]

### Step 2: Substitute the expression into the second equation
Now we substitute the expression for \( x \) into the second equation:
\[ 3x + 2y = 4 \]
Substituting \( x \):
\[ 3\left(\frac{9 - 5y}{8}\right) + 2y = 4 \]

### Step 3: Simplify the equation
Now we simplify the equation:
\[ \frac{27 - 15y}{8} + 2y = 4 \]
To eliminate the fraction, multiply the entire equation by 8:
\[ 27 - 15y + 16y = 32 \]

### Step 4: Combine like terms
Now combine the terms:
\[ 27 + y = 32 \]

### Step 5: Solve for \( y \)
Subtract 27 from both sides:
\[ y = 32 - 27 \]
\[ y = 5 \]

### Step 6: Substitute back to find \( x \)
Now that we have \( y \), we substitute it back into the expression we found for \( x \):
\[ x = \frac{9 - 5(5)}{8} \]
\[ x = \frac{9 - 25}{8} \]
\[ x = \frac{-16}{8} \]
\[ x = -2 \]

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