Solve the following system of equations using the cross multiplication method.

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Solution

Step 1:Applyling & Analysing
The given system of equations may be written as
$a x + b y - k = 0 c x - d y - l = 0$
The given system of equation is of the forms
$a_{1} x + b_{1} y + c_{1} = 0 a_{2} x + b_{2} y + c_{2} = 0$
Step 2: Using cross multiplication method
the equation is,
$x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}} y = \frac{c_{1} a_{2} - c_{2} b_{1}}{a_{1} b_{2} - a_{2} b_{1}} w h e r e, a_{1} = a, b_{1} = b, c_{1} = - k a_{2} = c, b_{2} = - d, c_{2} = - l x = \frac{b x - l - - d x - k}{a x - d - c x b} = \frac{- b l - d k}{- a d - c d} = \frac{- b l - d k}{a d - c d} y = \frac{- k c + a l}{- a d - c b}$
Hence $x = \frac{- b l - d k}{- a d - c d} & y = \frac{- k c + a l}{- a d - c b}$ is the required solution of the given equation

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