Question 43

If $$x - y = -6$$ and $$x + y = 16$$, then $$x^2 - y^2$$ is?

Solution

Equation (i) : $$x - y = -6$$

Equation (ii) : $$x + y = 16$$

Adding above equations, we get : $$2x = -6 + 16 = 10$$

=> $$x = \frac{10}{2} = 5$$

Substituting value of x in equation (ii), => $$y = 16 - 5 = 11$$

$$\therefore$$ $$x^2 - y^2 = (5)^2 - (11)^2$$

= $$25 - 121 = -96$$

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