For the given pair of linear equations a 1 x - b 1 y - c 1-0 and a 2 x - b 2 y - c 2-0- the solution x - y isA- b2 C2-b1 c1 -a1 b2-a2 b1-c2 a2-c1 a1 -a1 b2-a2 b1B- None of theseC- b 2 C 1- b 1 c 2 - a 1 b 2- a 2 b 1- c 1 a 1- c 2 a 2 - a 1 b 2- a 2 b 1D- b1 C2-b2 c1 -a1 b2-a2 b1-c1 a2-c2 a1 -a1 b2-a2 b1

The correct option is D ((b1c2 b2c1)/(a1b2 a2b1), (c1a2 c2a1)/(a1b2 a2b1)) Let us use Elimination method to solve the given pair of equations Given two equati ...

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Standard X

Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

For the given...

Question

For the given pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0,$ the solution $(x, y)$ is

((b₁c₂-b₂c₁)/(a₁b₂-a₂b₁), (c₁a₂-c₂a₁)/(a₁b₂-a₂b₁))

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((b₂c₂-b₁c₁)/(a₁b₂-a₂b₁), (c₂a₂-c₁a₁)/(a₁b₂-a₂b₁))

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((b₂c₁-b₁c₂)/(a₁b₂-a₂b₁), (c₁a₁-c₂a₂)/(a₁b₂-a₂b₁))

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None of these

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Solution

The correct option is A
((b₁c₂-b₂c₁)/(a₁b₂-a₂b₁), (c₁a₂-c₂a₁)/(a₁b₂-a₂b₁))

Let us use Elimination method to solve the given pair of equations

Given two equations are $a_{1} x + b_{1} y + c_{1} = 0$

and $a_{2} x + b_{2} y + c_{2} = 0$

Multiply first equation by $b_{2}$ and second equation by $b_{1}$ , to get

$b_{2} a_{1} x + b_{2} b_{1} y + b_{2} c_{1} = 0$
$b_{1} a_{2} x + b_{1} b_{2} y + b_{1} c_{2} = 0$

Subtracting these two equations

( $b_{2}$ $a_{1}$ – $b_{1}$ $a_{2}) x$ + ( $b_{2}$ $b_{1}$ – $b_{1}$ $b_{2}) y$ + ( $b_{2}$ $c_{1}$ – $b_{1}$ $c_{2}$ ) = 0

i.e., ( $b_{2}$ $a_{1}$ – $b_{1}$ $a_{2}) x$ = $b_{1}$ $c_{2}$ – $b_{2}$ $c_{1}$

Therefore $x = \frac{(b_{1} c_{2} - b_{2} c_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ ,

Substitute this x in any of the given equation we get

$y = \frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$

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Similar questions

The solution (x,y) for the given pair of linear equations is $a_{1}$ x + $b_{1}$ y + $c_{1}$ =0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ =0

Q. For the given pair of linear equations,

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

.

The values of x and y are ( __ , __ ). Fill in the blanks

For the pair of linear equations $a_{1} x$ + $b_{1} y$ + $c_{1} = 0$ and $a_{2} x$ + $b_{2} y$ + $c_{2} = 0$ , the solution set are $x = \frac{(b_{1} c_{2} - b_{2} c_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ and $y = \frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ . They can also be written as:

The solution set x= $\frac{(b_{1} c_{2} - b_{2} c_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ and y= $\frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ to the pair of linear equations $a_{1}$ x + $b_{1}$ y + $c_{1}$ =0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ =0 can be written as

Solve the two equations using method of elimination.

$a_{1} x + b_{1} y + c_{1} = 0$
$a_{2} x + b_{2} y + c_{2} = 0$

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For the given pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0, the solution (x,y) is

For the given pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0,$ the solution $(x, y)$ is