If $2x + 3y = 26$ and $y-x=2$, then the value of $x + y$ is:

10

The correct answer is Option (2) → 10

1. Set up the Equations

We are given two equations:

1. $2x + 3y = 26 \quad \text{--- (Equation 1)}$
2. $y - x = 2 \quad \text{--- (Equation 2)}$

2. Solve for $y$ in terms of $x$

From Equation 2, we can express $y$ as:

$y = x + 2$

3. Substitute and Solve for $x$

Substitute the value of $y$ into Equation 1:

$2x + 3(x + 2) = 26$

$2x + 3x + 6 = 26$

$5x + 6 = 26$

$5x = 20$

$x = 4$

4. Find the value of $y$

Substitute $x = 4$ back into the expression for $y$:

$y = 4 + 2$

$y = 6$

5. Calculate $x + y$

Now, add the values of $x$ and $y$:

$x + y = 4 + 6 = 10$