Question

x+y=a+b,
ax-by=a²-b²

solve for x and y.........
plz answer fast​

Answer 1

$\LARGE\underline{\underline{\mathfrak{\green{AnSwEr}}}}$

$\bold{\red{\:Given\:here\begin{cases} (x+y = a+b)&\text{equ.(1)} \\ (ax - by = a^2 - b2 )&\text{equ. (2)}\end{cases}}}$

$\LARGE\underline\mathfrak{\pink{ExPlaNaTiOn}}$

$\:\mathrm{(multiply \:by \:a\:in\:\:equ.(1)}$

$\leadsto\mathrm{\:ax+ay\:=\:a^2+ab}$

$\:\:\mathrm{\:write\:here\:both\:equ}$

• $\green{\mathrm{\:ax+ay\:=\:a^2+ab}}$
• $\green{\mathrm{\:ax-by\:=\:a^2-b^2}}$

$\:\:\:\:\:\:\:\green{\mathrm{\:(subtract\:its)}}$

______________________________

$\leadsto\mathrm{\:y(a+b)\:=\:(b^2+ab)}$

$\leadsto\mathrm{\:y\:=\frac{(b^2+ab)}{(a+b)}}$

$\:\:\:\:\:\:\red{\mathrm{(taking\:b\:common)}}$

$\leadsto\mathrm{\:y\:=\frac{b\cancel{(a+b)}}{\cancel{(a+b)}}}$

$\leadsto\mathrm{\red{\boxed{\green{\:y\:=\:b}}}}$

$\:\:\:\:\red{\mathrm{\:keep\:value\:of\:y\:in\:equ(1)}}$

$\leadsto\mathrm{\:(x+b)\:=\:(a+b)}$

$\leadsto\mathrm{\:x\:=\:a+\cancel{b}-\cancel{b}}$

$\leadsto\mathrm{\green{\boxed{\red{\:x\:=\:a}}}}$

Thus:-

• $\pink{\textrm{\:value\:of\:x\:=\:a}}$
• $\pink{\textrm{\:value\:of\:y\:=\:b}}$

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Answer 2

Step-by-step explanation:

exam to khatam ho chuka he