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

ICSE BoardEnglish MediumSTD 9MATHEMATICSSimultaneous (Linear) Equations (Including Problems)3 Marks
Question
Solve, using cross-multiplication :$3x + 4y = 11,2x + 3y = 8$
✓

Answer

Given equations are $3 x+4 y=11$ and $2 x+3 y=8$
Comparing with $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$,
 we have
$a_1=3, b_1=4, c_1=-11$  and  $a_2=2, b_2=3, c_2=-8$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow x=\frac{4 \times(-8)-3 \times(-11)}{3 \times 3-2 \times 4}$ and $y=\frac{-11 \times 2-(-8) \times 3}{3 \times 3-2 \times 4}$
$\Rightarrow x=\frac{-32+33}{9-8}$  and  $y=\frac{-22+24}{9-8}$
$\Rightarrow x=1$ and $y=2$

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