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

Step 1: Multiply the first equation

To eliminate one of the variables, we can multiply the first equation by 3. This will make the coefficient of $y$ in the first equation equal in magnitude and opposite in sign to the coefficient of $y$ in the second equation.

Step 2: Add the modified equations

Now, add the modified first equation to the second equation. The $y$ terms will cancel out, allowing us to solve for $x$.

Step 3: Solve for x

Divide both sides of the equation by 5 to find the value of $x$.

Step 4: Substitute x into the first equation

Substitute the value of $x$ back into the original first equation ($x + y = 5$) to solve for $y$.

Step 5: Solve for y

Subtract $\frac{19}{5}$ from 5 to find the value of $y$. Convert 5 to a fraction with a denominator of 5 to perform the subtraction.

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