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Simultaneous (Linear) Equations (Including Problems) — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSSimultaneous (Linear) Equations (Including Problems)4 Marks
Question
Solve, using cross-multiplication $:4x - y = 5,5y - 4x = 7$
✓

Answer

Given equation are $4 x-y=5$ and $5 y-4 x=7$
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
$a_1=41, b_1=-1, c_1=-5$  and $a_2=-4, b_2=5, c_2=-7$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow \mathrm{x}= \frac{-1 \times(-7)-5 \times(-5)}{4 \times 5-(-4) \times(-1)}$ and $y=\frac{(-5) \times(-4)-(-7) \times 4}{4 \times 5-(-4) \times(-1)}$
$\Rightarrow x=\frac{7+25}{20-4}$  and $y=\frac{20+28}{20-4}$
$ \Rightarrow \mathrm{x}=\frac{32}{16}$  and  $y=\frac{48}{16}$
$ \Rightarrow \mathrm{x}=2$  and $\mathrm{y}=3$

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