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Question

Solve for xandy

x+y=a-b;ax-by=a2+b2


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Solution

Step 1:Simplification to make the'y' coefficient as same

x+y=a-b...................................(1)ax-by=a2+b2...............................(2)

Equation (1) ×b

Equation(1)bx+by=ab-b2.................................(3)Equation(2)ax-by=a2+b2..........................................(2)

Step 2: Applying elimination method to find the value of x

equation(2)+(3)ax+bx=a2+abx(a+b)=a(a+b)x=a(a+b)a+bx=a

Step 3:Finding the value of 'y'by substitution method

Substitutethevalueofx=ainequation(1)Equation(1)a+y=a-by=a-b-ay=-b

Therefore the values ofx=aandy=-b


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