Question

solve x+y-(a+b)=0 and ax-by-(a2 - b2)=0 by cross multiplication ​

Answer 1

x = a, y = b

Step-by-step explanation:

Given that,

x + y - (a+b) = 0

ax - by - (a^2 - b^2) = 0

Using cross-multiplication, we get:

$\frac{x}{- (a^2 - b^2) - (-b) * -(a + b) }$ = $\frac{-y}{- (a^2 - b^2) - a * -(a + b) }}$ = $\frac{1}{1 * -b -a * 1}$

⇒ $\frac{x}{- a^2 + b^2 - ab - b^2 }$ = $\frac{-y}{- a^2 + b^2 + a^2 + ab } = \frac{1}{-b-a}$

⇒ $\frac{x}{-a(a + b)} = \frac{-y}{b(a + b)} = \frac{1}{- (a + b)}$

⇒ $\frac{x}{-a(a + b)} = \frac{y}{-b(a + b)} = \frac{1}{- (a + b)}$

⇒ x = $\frac{-a(a + b)}{-(a + b)}$ = a & y = $\frac{-b(a + b)}{-(a + b)}$ = b

∵ x = a & y = b

Learn more: Find the value of x

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