Question

find the value of x nd y by of substitution.method
3. x + y = a - b
ax - by = a2 + b2
​

Answer 1

find the value of x nd y by of substitution.method

3. x + y = a - b

ax - by = a2 + b2

★ Solution.

multiply by "b" in 1st equation we get,

$\tt\implies bx +by+=ab-b^2$

$\rule{230}2$

$\implies\tt ax - by = a2 + b2\\\implies\tt\frac{bx +by+=ab-b^2 }<u>{ax - by = a2 + b2}</u>\\\implies\tt (a+b)x=ab+a^2\\\implies\tt x=\frac{ab+a^2}{a+b}\\\implies\tt \frac{ab+a^2}{a+b}+y=a-b\\\implies\tt y=a-b-\frac{ab-a^2}{a+b}\\\implies\tt \frac{a^2-b^2-ab-ab-a^2}{a+b}(a^2\:and\:a^2\:get\: cancelled\:out)\\\implies\tt y=-\frac{b^2-2ab}{a+b}$