Solve the following pair of linear equations by the cross-multiplication method and find the values of x and y respectively: x+2y=2 and x-3y=7

# Solve the following pair of linear equations by the cross-multiplication method and find the values of x and y respectively: x+2y=2 and x-3y=7

1. A
4,-1
2. B
-1,4
3. C
2,3
4. D
1,1

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### Solution:

Given that the pair of linear equations   and  .
To solve the equations   and   by cross multiplication method, arrange the variables and the coefficients   and   and the constants   then ${x}{=}\frac{{{b}}_{{1}}{{c}}_{{2}}{-}{{b}}_{{2}}{{c}}_{{1}}}{{{a}}_{{1}}{{b}}_{{2}}{-}{{a}}_{{2}}{{b}}_{{1}}}$  and $y=\frac{{a}_{2}{c}_{1}-{a}_{1}{c}_{2}}{{a}_{1}{b}_{2}-{a}_{2}{b}_{1}}$ will be the required values of x and y.
Here,
Putting the values to find the value of x,
$⇒$ ${x}{=}\frac{{2}{×}{\left(}-7\right){-}{\left(}{-}{3}{\right)}{×}{\left(}{-}{2}{\right)}}{{1}{×}{\left(}{-}{3}{\right)}{-}{1}{×}{2}}$
$⇒$ $x=\frac{-14-6}{-3-2}$
$⇒$ $x=\frac{-20}{-5}$
$⇒$ ${x}{=}{4}$
Putting the values to find the value of y,
$⇒$ ${y}{=}\frac{{\left(}1{\right)}{×}\left(-2\right){-}{\left(}1{\right)}{×}\left(-7\right)}{{1}{×}\left(-3\right){-}{1}{×}{2}}$
$⇒$ $y=\frac{-2+7}{-3-2}$
$⇒$ $y=\frac{5}{-5}$

Therefore, the value of x is 4 and the value of y is -1.
Hence, option (1) is correct.

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