Question

ax+by=c, bx+ay=(1+c)

SOLVE THE FOLLOWING SYSTEM OF EQUATION BY USING SUBSTITUTION METHOD AND ELIMINATION METHOD ! ​

Answer 1

Step-by-step explanation:

Given equations are,

ax+by=c ....(1)

and bx+ay=1+c ....(2)

Multiply equation (1) by a and equation (2) by b, we get

a

2

x+aby=ac ....(3)

and b

2

x+aby=b+bc ....(4)

Subtract equations (3) and (4),

x(a

2

−b

2

)=ac−b−bc

⇒x=

a

2

−b

2

ac−b−bc

Put this value in equation (1), we get

a(

a

2

−b

2

ac−b−bc

)+by=c

⇒a

2

c−ab−abc−a

2

c+b

2

c=−by(a

2

−b

2

)

⇒b(bc−ab−a)=−by(a

2

−b

2

)

⇒y=

b

2

−a

2

bc−a−ac