Question

Solve:
I)ax+by=a-b
bx-ay=a+b
Ii) ax+by=bx+ay=1+c
Note: Simultaneous Equation.
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Answer 1

Answer:

Given equations are,

ax+by=a−b     ...(i)

bx−ay=a+b     ...(ii)

Multiplying eq (i) by a and eq (ii) by b, we get

a(ax+by)=a(a−b)

⇒a  

2

x+aby=a  

2

−ab      ...(iii)

b(bx−ay)=b(a+b)

⇒b  

2

x−aby=ab+b  

2

      ...(iv)

Adding eq (iii) and eq(iv)  

  a  

2

x+aby=a  

2

−ab

  b  

2

x−aby=ab+b  

2

 

(a  

2

+b  

2

)x=(a  

2

+b  

2

)

​

 

⇒x=  

(a  

2

+b  

2

)

(a  

2

+b  

2

)

​

 

⇒x=1

Substituting the value of x in eq (i), we get

a×1+by=a−b

⇒a+by=a−b

⇒by=−b

⇒y=−  

b

b

​

 

⇒y=−1

Hence x=1  and  y=−1.