Download App

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

ICSE BoardEnglish MediumSTD 9MATHEMATICSSimultaneous (Linear) Equations (Including Problems)4 Marks
Question
Solve, using cross$-$multiplication $:\sqrt2x - \sqrt3y = 0,\sqrt5x + \sqrt2y = 0$
✓

Answer

Given equation are $\sqrt{2 } x-\sqrt{3 } y=0$ and $\sqrt{ 5} x+\sqrt{2 } y=0$
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
$a_1=\sqrt{2}, b_1=\sqrt{ 3} , c_1=0$ and $a_2=\sqrt{5}, b_2=\sqrt{2 } , c_2=0$
Now, $x=\frac{b_1 c_2-b_2 c_1}{a_1 b_2-a_2 b_1}$ and $y=\frac{c_1 a_2-c_2 a_1}{a_1 b_2-a_2 b_1}$
$\Rightarrow \mathrm{x}=$
$\frac{(-\sqrt{3}) \times 0-\sqrt{2} \times 0}{\sqrt{2} \times \sqrt{2}-\sqrt{5} \times(-\sqrt{3})}$ and $y=\frac{0 \times \sqrt{5}-0 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}-\sqrt{5} \times(-\sqrt{3})}$
$\Rightarrow x=\frac{0}{2+\sqrt{15}}$ and $y=\frac{0}{2+\sqrt{15}}$
$\Rightarrow x=0$ and $y=0$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Simultaneous (Linear) Equations (Including Problems)→Simultaneous (Linear) Equations (Including Problems) — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Simplify by rationalising the denominator in the following.$\frac{5+\sqrt{6}}{5-\sqrt{6}}$
→
A square plate of side $'x\ ' \ cm$ is $4\ mm$ thick. If its volume is $1440 \ cm^3$; find the value of $'x\ '.$
→
Given: $\sec\ A=\frac{29}{21}$, evaluate $: \sin A -\frac{1}{\tan A }$
→
Solve :$4 x+\frac{6}{y}=15$ and $3 x-\frac{4}{y}=7$. Hence, find $a$ if $y=a x-2$
→
$D$ is a point in side $BC$ of $\triangle ABC.$ If $AD > AC$, show that $AB > AC.$
→
Write two rational numbers between $\sqrt{3}$ and $\sqrt{7}$
→
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric. $\tan C=\frac{5}{12}$
→
The ten’s digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is $32$. Find the number.
→
In an equilateral $\triangle ABC$; points $P, Q$ and $R$ are taken on the sides $AB, BC$ and $CA$ respectively such that $AP = BQ = CR$. Prove that $\triangle PQR$ is equilateral.
→
Evaluate the following:$9^4 \div 27^{-\frac{2}{3}}$
→