Solve the following system of equations using the cross multiplication method.
$21 x = 13 y + 21, 4 x + 7 y - 20 = 0$

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Solution

Step 1:Applying and Analysing
The given system of equations may be written as
$21 x - 13 y - 21 = 0 4 x + 7 y - 20 = 0$
The given system of equation is of the form
$a_{1} x + b_{1} y + c_{1} = 0 a_{2} x + b_{2} y + c_{2} = 0$
Step 2: Using cross multiplication method.
The equation is,
$x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}} W h e r e, a_{1} = 21, b_{1} = - 13, c_{1} = - 21 a_{2} = 4, b_{2} = 7, c_{2} = - 20 x = \frac{- 13 x - 20 - 7 x - 13}{21 x 7 - 4 x - 13} = \frac{260 + 147}{147 + 52} = \frac{407}{199} = 2 \frac{9}{199} y = \frac{- 21 x 4 - - 20 x 21}{21 x 7 - 4 x - 13} = \frac{- 84 + 420}{147 + 52} = \frac{336}{199} = 1 \frac{137}{199}$
Hence $x = 2 \frac{9}{199} & y = 1 \frac{137}{199}$ is thge required solution.

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