Algebraic Algebra III

$x - y = 22$ $(1)$

$6x + 5y = 253$ $(2)$

Multiply equation $(1)$ by $5$ :

$5x - 5y = 110$ $(3)$

$6x + 5y = 253$ $(2)$

Add the equations:

$11x = 363$

$\frac{11x}{11}$ $=$ $\frac{363}{11}$

$x =$ $\frac{363}{11}$

$x = 33$

Substitute $x = 33$ into equation $(1)$ :

$33 - y = 22$

$-y = 22 - 33 = -11$

$y = 11$

Check by substituting the values into the other set of equations:

$33 - 11 = 22 = 22$

$\frac{33}{11}$ $= 3$

$3 + 24 = 27 = 27$

Therefore $x = 33, y = 11$ .

Since we are requested to give our answer in the form $x + y$ :

$33 + 11 = \fbox{44}$