Question

Solve the following pair of linear eqns by elimination method (Class X)
ax + by = (a-b)
bx - ay = (a+b)​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• ax + by = (a - b)---------Equ(1)
• bx - ay = (a+b) ----------Equ(2)

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• Value of x & y

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Solution By, Elimination Method

multiply by b in equ(1) & a in equ(2)

• abx + b²y = (ab - b²)
• abx - a²y = (a² +ab)

______________Sub. it's (Eliminate x)

➥ b²y + a²y = (ab-b²)-(a²+ab)

➥ y(a²+b²) = (ab - ab - a² - b²)

➥ y(a²+b²) = -(a²+b²)

➥ y = -(a²+b²)/(a²+b²)

➥y = -1

Keep Value of y in equ(1)

➥ ax + b * (-1) = (a - b)

➥ ax = a - b + b

➥ ax = a

➥ x = a/a

➥ x = 1

________________________

$\Large{\underline{\mathfrak{\bf{Hence}}}}$

• Value of x = 1
• Value of y = -1

_________________

$\Large{\underline{\underline{\mathfrak{\bf{Answer\:Verification}}}}}$

For this, Keep Value of x & y in equ(1)

➥ a * 1 + b * (-1) = a - b

➥ a - b = a - b

L.H.S. = R.H.S.

Again,

Keep Value of x & y in equ(2),

➥ b *1 - a * (-1) = a + b

➥ a + b = a + b

L.H.S. = R.H.S.

That's Proved

_______________