x+ay=1, ax-y=3 (solve by substitution method)
Answers
Step-by-step explanation:
x = b & y = -a
Step-by-step explanation:
Given system of equations:
\frac{ax}{b}-\frac{by}{a}=a+b
b
ax
−
a
by
=a+b ...................... (1)
ax-by=2abax−by=2ab ....................(2)
from equation (2), we get
ax=2ab+byax=2ab+by
x=\frac{2ab+by}{a}x=
a
2ab+by
......... (3)
Put, this value of eqn (3) in eqn(1)
\frac{a\times\frac{2ab+by}{a}}{b}-\frac{by}{a}=a+b
b
a×
a
2ab+by
−
a
by
=a+b
\frac{2ab+by}{b}-\frac{by}{a}=a+b
b
2ab+by
−
a
by
=a+b
\frac{a(2ab+by)-b^2y}{ab}=a+b
ab
a(2ab+by)−b
2
y
=a+b
2a^2b-aby+b^2y=ab(a+b)2a
2
b−aby+b
2
y=ab(a+b)
2a^2b+(ab-b^2)y=a^2b+ab^22a
2
b+(ab−b
2
)y=a
2
b+ab
2
(ab-b^2)y=a^2b+ab^2-2a^2b(ab−b
2
)y=a
2
b+ab
2
−2a
2
b
b(a-b)y=ab^2-a^2bb(a−b)y=ab
2
−a
2
b
b(a-b)y=-ab(a-b)b(a−b)y=−ab(a−b)
y=\frac{-ab(a-b)}{b(a-b)}y=
b(a−b)
−ab(a−b)
y=-ay=−a
Now, Put value of y in eqn (3)
x=\frac{2ab-ba}{a}x=
a
2ab−ba
x=\frac{ab}{a}x=
a
ab
x=bx=b
Therefore, x = b & y = -a