ax+by = 3ab
a²x + b²y=a+b
find x and y
Answers
Step-by-step explanation:
ax+by=3ab...(i)
{a}^{2} x + {b}^{2} y = a + b...(ii)a
2
x+b
2
y=a+b...(ii)
y = \frac{a(3b - x)}{b} ...from(i)y=
b
a(3b−x)
...from(i)
substitute \: the \: value \: of \: x \: in \: (ii) \: we \: get \:substitutethevalueofxin(ii)weget
{a}^{2} x + {b}^{2} \frac{a(3b - x)}{b } = a + ba
2
x+b
2
b
a(3b−x)
=a+b
{a}^{2} x + 3a {b}^{2} - abx = a + ba
2
x+3ab
2
−abx=a+b
x = \frac{a + b - 3a {b}^{2} }{ {a}^{2 -}ab }x=
a
2−
ab
a+b−3ab
2
therefore \: y = \frac{a(3b - x)}{b}thereforey=
b
a(3b−x)
= \frac{a(3b - \times \frac{a + b - 3a {b}^{2} }{ {a}^{2} - ab} )}{b}=
b
a(3b−×
a
2
−ab
a+b−3ab
2
)
= \frac{(3 {a}^{2} b - 3a {b}^{2} - a - b + 3a {b}^{2} )}{b (a - b)}=
b(a−b)
(3a
2
b−3ab
2
−a−b+3ab
2
)
= \frac{3 {a}^{2} b - a - b}{b(a - b)}=
b(a−b)
3a
2
b−a−b