Question
Solve, using cross$-$multiplication $:8x + 5y = 9,3x + 2y = 4$
✓
Answer
Given equation are $8 x+5 y=9$ and
$3 x+2 y=4$
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
$a_1=8, b_1=5, c_1=-9$ and $a_2=3, b_2=2, c_2=-4$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow \mathrm{x}=\frac{5 \times(-4)-2 \times(-9)}{8 \times 2-3 \times 5}$ and $y=\frac{-9 \times 3-(-4) \times 8}{8 \times 2-3 \times 5}$
$ \Rightarrow \mathrm{x}=\frac{-20+18}{16-15}$ and $y=\frac{-27+32}{16-15}$
$ \Rightarrow \mathrm{x}=-\frac{2}{1}$ and $y=\frac{5}{1}$
$ \Rightarrow \mathrm{x}=-2$ and $\mathrm{y}=5 .$
$3 x+2 y=4$
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
$a_1=8, b_1=5, c_1=-9$ and $a_2=3, b_2=2, c_2=-4$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow \mathrm{x}=\frac{5 \times(-4)-2 \times(-9)}{8 \times 2-3 \times 5}$ and $y=\frac{-9 \times 3-(-4) \times 8}{8 \times 2-3 \times 5}$
$ \Rightarrow \mathrm{x}=\frac{-20+18}{16-15}$ and $y=\frac{-27+32}{16-15}$
$ \Rightarrow \mathrm{x}=-\frac{2}{1}$ and $y=\frac{5}{1}$
$ \Rightarrow \mathrm{x}=-2$ and $\mathrm{y}=5 .$
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