Given the linear equation 2x + 3y - 8 = 0, write another linear e… - Vidyadip

Question

Given the linear equation $2x + 3y - 8 = 0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

Intersecting lines.
Parallel lines.
Coincident lines.

✓

Answer

For the two lines $a_1x + b_1x + c_1 = 0$ and $a_2x + b_2x + c_2 = 0$, to be intersecting, we must have
$\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
So, the other linear equation can be $5x + 6y - 16 = 0$
as $\frac{\text{a}_1}{\text{a}_2}=\frac{2}{5},$
$\frac{\text{b}_1}{\text{b}_2}=\frac{3}{6}=\frac{1}{2},$
$\frac{\text{c}_1}{\text{c}_2}=\frac{-8}{-16}=\frac{1}{2}$
For the two lines $a_1x + b_1x + c_1 = 0$ and $a_2x + b_2x + c_2 = 0$, to be parallel, we must have
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
So, the other linear equation can be $6x + 9y + 24 =0$
as $\frac{\text{a}_1}{\text{a}_2}=\frac{2}{6}=\frac{1}{3},$
$\frac{\text{b}_1}{\text{b}_2}=\frac{3}{9}=\frac{1}{3},$
$\frac{\text{c}_1}{\text{c}_2}=\frac{-8}{24}=\frac{-1}{3}$
For the two lines $a_1x + b_1x + c_1 = 0$ and $a_2x + b_2x + c_2 = 0$, to be coincident, we must have
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$
So, the other linear equation can be $8x + 12y - 32 =0$
as $\frac{\text{a}_1}{\text{a}_2}=\frac{2}{8}=\frac{1}{4},$
$\frac{\text{b}_1}{\text{b}_2}=\frac{3}{12}=\frac{1}{4},$
$\frac{\text{c}_1}{\text{c}_2}=\frac{-8}{-32}=\frac{1}{4}$

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 Questions" 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 sum of first $9$ terms of an A.P. is $162$. The ratio of its $6^{th}$ term to its $13^{th}$ term is $1 : 2$. Find the first and $15^{th}$ term of the A.P?

The following is the frequency distribution of blood pressure measured for 100 patients.

Blood pressure in suitable units.	110-115	115-120	120-125	125-130	130-135
No. of patients	2	35	52	8	3

Find the modal Blood pressure of the patient.

Mr. D'souza purchased 200 shares of FV Rs. 50 at a premium of Rs. 100. He received 50% dividend on the shares. After receiving the dividend he sold 100 shares at a discount of Rs. 10 and remaining shares were sold at a premium of Rs. 75. For each trade he paid the brokerage of Rs. 20. Find whether Mr. D'souza gained or incurred a loss? by how much?

If the mean of the following frequency distribution is 24, find the value of p.

Class	0-10	10-20	20-30	30-40	40−50
Frequency	3	4	p	3	2

Find the roots of the following quadratic equation (if they exist) by the method of completing the square.
$2\text{x}^2-7\text{x}+3=0$

Prove that the square of any positive integer is of the form $3m$ or, $3m + 1$ but not of the from $3m + 2.$

The difference of two natural numbers is $5$ and the difference of their reciprocals is $\frac{5}{14}.$ Find the numbers.

Solve the following systems of equations graphically:

What is the probability than an ordinary year has 53 Sundays?

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of the point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another points D such that ABCD is a rhombus.