Solve: (a+2b)x + (2a-b)y=2 (a-2b)x + …

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Solve:

(a+2b)x + (2a-b)y=2

(a-2b)x + (2a+B)y =3

Posted by Gyayak Jain 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

The given system of equations are :
(a + 2b)x + (2a - b)y = 2
So, (a + 2b)x + (2a - b)y - 2 = 0 ............(i)
And (a - 2b) x + (2a + b) y = 3
So, (a - 2b)x + (2a + b)y - 3 = 0 .........(ii)
The given equations is in the form of
a₁x + b_1y + c₁ = 0
and a₂x + b_2y + c₂ = 0
So, we get
a₁ = a + 2b, b₁ = 2a - b, c₁ = -(2)
a₂ = a - 2b, b₂ = 2a + b, c₂ = (-3)
By cross-multiplication method:
$\frac{x}{{ - 2a + 5b}} = \frac{y}{{a + 10b}} = \frac{1}{{10ab}}$
Now, $\frac{x}{{ - 2a + 5b}} = \frac{1}{{10ab}}$
$⇒ x = \frac{{5b - 2a}}{{10ab}}$
And $\frac{y}{{a + 10b}} = \frac{1}{{10ab}}$
$⇒ y = \frac{{a + 10b}}{{10ab}}$
The solution of the system of equations are $x = \frac{{5b - 2a}}{{10ab}}$ and $y = \frac{{a + 10b}}{{10ab}}$ respectively.

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