Question

Solve the following pair of linear equations by eliminition method:
1. ax+by=c
bx+ay=1+c
2. (a-b)x+(a+b)y=a²-2ab-b²
(a+b)(x+y)=a²+b²

Please provide answers with photo.

Answer 1

1.ax + by = c; bx + ay = (1 + c)

ax + by = c
bx + ay = (1+ c)
abx + b2y = bc
abx + aby = a(1+c)
(-)   (-)        (-)       
(b2 - ab)y = bc - a(1 + c)

y = [bc - a(1 + c)] / (b2 - ab)

ax + by = c
ax + b[bc - a(1 + c)] / (b2 - ab) = c
ax = c - [b2c - ab(1 + c)] / (b2 - ab)
x = [c - b2c - ab(1 + c)] / (b2 - ab) / a


2.Sol:
(a-b)x + (a+b)y = a² - 2ab - b² -------------- (1)
(a+b)(x+y) = a² + b²
⇒ (a+b)x + (a+b)y = a² + b² ---------------- (2)
Solving equations 1 and 2, we get
x = (a+b)
Substituting the value of x in equation 2, we get
y = -2ab / (a+b)