ax+by=c
bx+ay=1+c
solve the pair of linear equation.
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Answer:
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
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