In the following system of equation determine whether the system … - Vidyadip

Question

In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

$x - 2y = 8$

$5x - 10y = 10$

✓

Answer

Given
$x - 2y = 8$
$5x - 10y = 10$
To find: To determine whether the system has a uniqfue solution, no solution or infinitely many solutions
We know that the system of equations,
$a_1x + b_1y + c_1 = 0$
$a_2x + b_2y + c_2 = 0$
For unique solution
$\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
For no solution
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
For infinitely many solution
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$
Here,
$\frac{1}{5}=\frac{-2}{-10}=\frac{8}{10}$
$\frac{1}{5}=\frac{1}{5}\neq\frac{4}{5}$
Since, $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$ which means $\frac{1}{5}=\frac{1}{5}\neq\frac{4}{5}$ hence the system of equation has no solution.
Hence the system of equation has no solution.

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 "5 Marks Questions" from Linear Equations in Two Variables→Linear Equations in Two Variables — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

If the volumes of two bones are in the ratio of 1 : 4 and their iameters are in the ratio of 4 : 5, find the ratio of their heights.

A solid consisting of a right cone standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is $60 \ cm$ and its height is $180 \ cm,$ the radius of the hemisphere is $60 \ cm$ and height of the cone is $120 \ cm,$ assuming that the hemisphere and the cone have common base.

A bucket open at the top is in the form of a frustum of a cone with a capacity of $12308.8 cm^3$. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use $\pi=3.14$)

A hemispherical tank, full of water, is emptied by a pipe at the rate of $\frac{25}{7}$ litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3m?

Solve the following systems of equations graphically:

2x - 3y - 7 = 0

Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(-3, -1).

Draw a 'less than' ogive for the following frequency distribution:

Classes:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency:	7	14	13	12	20	11	15	8

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and the product of its zeros are 5, -2 and -24 respectively.

Find the number of metallic circular discs with 1.5cm base diameter and of height 0.2cm to be melted to form a right circular cylinder of height 10cm and diameter
4.5cm.

A man observes a car from the to of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower.