Solve the following pair of linear equations :
`x+y=5`
`2x-3y=4.`

Answer

To solve the given pair of linear equations:
\[ x + y = 5 \]
\[ 2x - 3y = 4 \]

**Step 1: Express \( y \) in terms of \( x \) using the first equation.**

From the first equation:
\[ x + y = 5 \]
\[ y = 5 - x \]

**Step 2: Substitute the expression for \( y \) into the second equation.**

Substitute \( y = 5 - x \) into the second equation:
\[ 2x - 3(5 - x) = 4 \]

**Step 3: Simplify the equation and solve for \( x \).**

Expand and simplify:
\[ 2x - 3(5 - x) = 4 \]
\[ 2x - 15 + 3x = 4 \]
\[ 2x + 3x - 15 = 4 \]
\[ 5x - 15 = 4 \]

Add 15 to both sides:
\[ 5x = 19 \]

Divide both sides by 5:
\[ x = \frac{19}{5} \]

**Step 4: Substitute the value of \( x \) back into the expression for \( y \).**

Substitute \( x = \frac{19}{5} \) into \( y = 5 - x \):
\[ y = 5 - \frac{19}{5} \]

Convert 5 to a fraction with a denominator of 5:
\[ y = \frac{25}{5} - \frac{19}{5} \]
\[ y = \frac{25 - 19}{5} \]
\[ y = \frac{6}{5} \]

**Final Solution:**

The solution to the pair of linear equations is:
\[ x = \frac{19}{5} \]
\[ y = \frac{6}{5} \]