Question

solve by cross multiplication method
a(x+y)-b(x-y)= a square-ab+ b square
a(x+y)-b(x-y)=a square +ab+ b squar
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Answer 1

(1) bx + cy = a + b, ax[1/(a-b) - 1/(a+b)] + cy[1/(b-a) - 1/(b+a)] = 2a/(a+b)

ax[1/(a-b) - 1/(a+b)] + cy[1/(b-a) - 1/(b+a)] = 2a / (a+b)

⇒ ax[(a + b - a + b)/(a2 - b2)] + cy[(b + a - b + a) /(b2 - a2)] = 2a / (a+b)

⇒ 2abx / (a2 - b2) + 2acy / (b2 - a2) = 2a / (a+b)

⇒ bx / (a2 - b2) + cy / (b2 - a2) = 1 / (a+b)

⇒ bx / (a2 - b2) - cy / (a2 - b2) = 1 / (a+b)

⇒ bx / (a - b) - cy / (a - b) = 1

⇒ (bx - cy) / (a - b) = 1

⇒ (bx - cy) = (a - b)

Consider the equations bx + cy - (a + b) = 0 and bx - cy - (a - b) = 0.

Solution of the equations using cross multiplication method:

a1 = b, b1 = c, c1 = -(a + b)

a2 = b, b2 = - c, c2 = -(a - b)

, 

x = -c(a - b) - c(a + b) / (-bc - bc), y = -b(a + b) + b(a - b) / (-bc - bc)

x = a/b, y = b/c.

2) (a-b)x + (a+b)y = 2a2 - 2b2, (a+b)(x+y) = 4ab

(a-b)x + (a+b)y - (2a2 - 2b2) = 0, (a+b)x + (a + b)y - 4ab = 0

Solution of the equations using cross multiplication method:

a1 = (a-b), b1 = (a+b), c1 = - (2a2 - 2b2)

a2 = (a+b), b2 = (a+b), c2 = - 4ab

Using the formula to get the values of x and y.

x = (a2 - b2 - 2ab) / (-b), y = (a - b)(a2 - b2) / b(b + a).

HOPE IT HELPS U....

Answer 2

Answer:

(1) bx + cy = a + b, ax[1/(a-b) - 1/(a+b)] + cy[1/(b-a) - 1/(b+a)] = 2a/(a+b)

ax[1/(a-b) - 1/(a+b)] + cy[1/(b-a) - 1/(b+a)] = 2a / (a+b)

⇒ ax[(a + b - a + b)/(a2 - b2)] + cy[(b + a - b + a) /(b2 - a2)] = 2a / (a+b)

⇒ 2abx / (a2 - b2) + 2acy / (b2 - a2) = 2a / (a+b)

⇒ bx / (a2 - b2) + cy / (b2 - a2) = 1 / (a+b)

⇒ bx / (a2 - b2) - cy / (a2 - b2) = 1 / (a+b)

⇒ bx / (a - b) - cy / (a - b) = 1

⇒ (bx - cy) / (a - b) = 1

⇒ (bx - cy) = (a - b)

Consider the equations bx + cy - (a + b) = 0 and bx - cy - (a - b) = 0.

Solution of the equations using cross multiplication method:

a1 = b, b1 = c, c1 = -(a + b)

a2 = b, b2 = - c, c2 = -(a - b)

,

x = -c(a - b) - c(a + b) / (-bc - bc), y = -b(a + b) + b(a - b) / (-bc - bc)

x = a/b, y = b/c.

2) (a-b)x + (a+b)y = 2a2 - 2b2, (a+b)(x+y) = 4ab

(a-b)x + (a+b)y - (2a2 - 2b2) = 0, (a+b)x + (a + b)y - 4ab = 0

Solution of the equations using cross multiplication method:

a1 = (a-b), b1 = (a+b), c1 = - (2a2 - 2b2)

a2 = (a+b), b2 = (a+b), c2 = - 4ab

Using the formula to get the values of x and y.

x = (a2 - b2 - 2ab) / (-b), y = (a - b)(a2 - b2) / b(b + a). HOPE IT HELPS U....