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solve the following pair of linear equations.(I)ax+by=a-b,bx-ay=a+b |
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Answer» ax+by=a-bax=a-b-byx=a-b-by/a←bx-ay=a+bsubstitutingb(a-b-by/a)-ay=a+bab-b²-b²y/a-ay=a+bab-b²-b²y-a²y/a=a+bab-b²-(b²+a²)y=a²+ab-(b²+a²)y=a²+ab-ab+b²(b²+a²)y=-(a²+b²)y=-(a²+b²)/a²+b²y=-1←substituting value of yx=a-b-b(-1)/ax=a-b+b/ax=a/ax=1 ax+by=a-bax=a-b-byx=a-b-by/a←bx-ay=a+bsubstitutingb(a-b-by/a)-ay=a+bab-b²-b²y/a-ay=a+bab-b²-b²y-a²y/a=a+bab-b²-(b²+a²)y=a²+ab-(b²+a²)y=a²+ab-ab+b²(b²+a²)y=-(a²+b²)y=-(a²+b²)/a²+b²y=-1←substituting value of yx=a-b-b(-1)/ax=a-b+b/ax=a/ax=1 |
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