Question

X+y=13and x-y=2 what is the value of x^2-y^2

Answer 1

Just a quick sidenote.

$\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ x+y=13\qquad x-y=2 \\\\\\ x^2-y^2\implies (x+y)(x-y)\implies (13)(2)$

Answer 2

X+y=13
x-y=2

Add the equations (elimination method)

x+y+x-y=13+2
2x=15
x=7.5

Plug in this y value

7.5-y=2
-y=-5.5
y=5.5

Plug in both the x and y values into the equation asked for

(7.5)^2-(5.5)^2
56.25-30.25

Final answer: 26