Question

Find the value of x and y...
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Answer 1

Given

$\bullet\ \; \rm ax+by=a-b\\\\\bullet\ \; \rm bx-ay=a+b$

To Find

Value of x and y

Solution

$\rm ax+by=a-b$

Multiply both sides by a ,

$\to \rm a(ax+by)=a(a-b)\\\\\to \rm a^2x+aby=a^2-ab...(1)$

$\rm bx-ay=a+b$

Multiply both sides by b ,

$\to \rm b(bx-ay)=b(a+b)\\\\\to \rm b^2x-aby=ab+b^2 ...(2)$

Solve (1) + (2) ,

$\to \rm a^2x+aby+b^2x-aby=a^2-ab+ab+b^2\\\\\to \rm a^2x+b^2x=a^2+b^2\\\\\to \rm x(a^2+b^2)=a^2+b^2\\\\\to \bf \pink{x=1\ \; \bigstar}$

Sub. x value in (1) ,

$\to \rm a^2(1)+aby=a^2-ab\\\\\to \rm a^2+aby=a^2-ab\\\\\to \rm aby=-ab\\\\\to \bf \green{y=-1\ \; \bigstar}$

Answer 2

Answer:

HOPE THIS HELPS BUDDY....