Download App

Linear Equations In Two Variables — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsLinear Equations In Two Variables3 Marks
Question
For what value of $\alpha,$ the system of equations will have no solution
$\alpha\text{x}+3\text{y}=\alpha-3$
$12\text{x}+\alpha\text{y}=\alpha$
 
✓

Answer

The given system of equations may be written as,
$\alpha\text{x}+3\text{y}-(\alpha-3)=0$
$12\text{x}+\alpha\text{y}-\alpha=0$
The given system of equations is of the form
$a_1x + b_1y + c_1 = 0$
$a_2x + b_2y + c_2 = 0$
Where, $\text{a}_1=\alpha,\text{b}_1=3,\text{c}_1=-(\alpha-3)$
and, $\text{a}_2=12,\text{b}_2=\alpha,\text{c}_2=-\alpha$
For no solution, we must have
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
$\Rightarrow\frac{\alpha}{12}=\frac{3}{\alpha}\neq\frac{-(\alpha-3)}{-\alpha}$
Now,
$\frac{3}{\alpha}\neq\frac{-(\alpha-3)}{-\alpha}$
$\Rightarrow\frac{3}{\alpha}\neq\frac{\alpha-3}{\alpha}$
$\Rightarrow3\neq\alpha-3$
$\Rightarrow3+3\neq\alpha$
$\Rightarrow6\neq\alpha$
$\Rightarrow\alpha\neq6$
and $\frac{\alpha}{12}=\frac{3}{\alpha}$
$\Rightarrow\alpha^2=36$
$\Rightarrow\alpha=\pm6$
$\Rightarrow\alpha=-6$ $\big[\therefore\alpha\neq6\big]$
Hence, the given system of equations will have no solution, if $\alpha=-6$

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 "3 Marks Question" from Linear Equations In Two Variables→Linear Equations In Two Variables — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

The roots of each of the following quadratic equation are real and equal, find k.
kx (x-2) + 6 = 0
→
The area of a rectangular plot is $462m^2$ and its length is $28\ m$. Find the perimeter of the plot.
→
Prove the following trigonometric identities.
$\cot\theta-\tan\theta=\frac{2\cos^2\theta-1}{\sin\theta\cos\theta}$
→
A dealer has given 10% discount on a showpiece of Rs. 25,000. GST of 28% was charged on the discounted price. Find the total amount shown in the tax invoice. What is the amount of CGST and SGST?
→
Find the LCM and HCF of the following integer by applying the prime factorisation method.
$84, 90$ and $120$
→
Find the coordinates of circumcentre and radius of circumcircle of triangle ABC ifA(7, 1), B(3, 5) and C(2, 0) are given.
→
A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each persion is equally likely to be selected, find the probability of selecting a person who is:
  1. Extermely patient.
  2. Extremely kind or honest. Which of the above values you prefer more.
→
Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right triangle.
→
A bucket is frustum shaped. Its height is $28 \mathrm{~cm}$. Radii of circular faces are $12 \mathrm{~cm}$ and $15 \mathrm{~cm}$. Find the capacity of the bucket. $\left(\pi=\frac{22}{7}\right.$ )
→
Prove the following trigonometric identities.
$\tan\theta-\cot\theta=\frac{2\sin^2\theta-1}{\sin\theta\cos\theta}$
→