In cross multiplication method of solving
$a_{1} x + b_{1} y + c_{1} = 0 a n d a_{2} x + b_{2} y + c_{2} = 0, x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}}$

True

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False

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Solution

The correct option is A True

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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

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

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:

When using cross multiplication method for solving

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

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

$x i s g i v e n b y \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}}$

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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In cross multiplication method of solving a1x+b1y+c1=0 and a2x+b2y+c2=0, x=b1c2−b2c1a1b2−a2b1

The correct option is A True

In cross multiplication method of solving
$a_{1} x + b_{1} y + c_{1} = 0 a n d a_{2} x + b_{2} y + c_{2} = 0, x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}}$