Solve, using cross-multiplication :6x + 7y - 11 = 0,5x + 2y = 13 - Vidyadip

Question

Solve, using cross$-$multiplication $:6x + 7y - 11 = 0,5x + 2y = 13$

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Answer

Given equation are $6 x+7 y-11=0$ and $5 x+2 y=13$
Comparing with $\mathrm{a}_1 \mathrm{x}+\mathrm{b}_1 \mathrm{y}+\mathrm{c}_1=0$ and $\mathrm{a}_2 \mathrm{x}+\mathrm{b}_2 \mathrm{y}+\mathrm{c}_2=0$,
We have
$a_1=6, b_1=7, c_1=-11$ and $a_2=5, b_2=2, c_2=-13$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow x= \frac{7 \times(-13)-2 \times(-11)}{6 \times 2-5 \times 7}$ and $y=\frac{-11 \times 5-(-13) \times 6}{6 \times 2-5 \times 7}$
$ \Rightarrow x=\frac{-91+22}{12-35}$ and $y=\frac{-55+78}{12-35}$
$ \Rightarrow x=\frac{-69}{-23}$ and $y=\frac{23}{-23}$
$ \Rightarrow x=3$ and $y=-1$

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