Question
Solve, using cross-multiplication$ :x - y + 2 = 0,7x + 9y = 130$
✓
Answer
Given equation are $x-y+2=0$ and $7 x+9 y=130$
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
$a_1=1, b_1=-1, c_1=2$ and $a_2=7, b_2=9, c_2=-130$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow x= \frac{-1 \times(-130)-9 \times 2}{1 \times 9-7 \times(-1)}$ and $y=\frac{2 \times 7-(-130) \times 1}{1 \times 9-7 \times(-1)}$
$\Rightarrow x=\frac{130-18}{9+7}$ and $y=\frac{14+130}{9+7}$
$\Rightarrow \mathrm{x}=\frac{112}{16} \quad$ and $y=\frac{144}{16}$
$\Rightarrow x=7$ and $y=9.$
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
$a_1=1, b_1=-1, c_1=2$ and $a_2=7, b_2=9, c_2=-130$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow x= \frac{-1 \times(-130)-9 \times 2}{1 \times 9-7 \times(-1)}$ and $y=\frac{2 \times 7-(-130) \times 1}{1 \times 9-7 \times(-1)}$
$\Rightarrow x=\frac{130-18}{9+7}$ and $y=\frac{14+130}{9+7}$
$\Rightarrow \mathrm{x}=\frac{112}{16} \quad$ and $y=\frac{144}{16}$
$\Rightarrow x=7$ and $y=9.$
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