Graphically, find whether the following pair of equations has no … - Vidyadip

Question

Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:
$5x - 8y + 1 = 0; ...(i)$
$3x -$ $\frac{24}{5}$$y$ $+$ $\frac{3}{5}$ $= 0 ...(ii)$

✓

Answer

$a_1 = 5,\ b_1 = -8,\ c_1 = 1$ and $a_2 = 3,\ b_2 =$ $\frac{-24}{5}$, $c_2 =$ $\frac{3}{5}$
$\frac { a _ { 1 } } { a _ { 2 } }$ = $\frac{5}{3}$$...(i)$
$\frac { b _ { 1 } } { b _ { 2 } }$ =$\frac { - 8 } { - 24 / 5 }$ = $\frac{5}{3}$$ ...(ii)$
and $\frac { c _ { 1 } } { c _ { 2 } }$ = $\frac { 1 } { 3 / 5 }$ = $\frac{5}{3}$ $...(iii)$
Form $(i), (ii)$ and $(iii)$
$\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } = \frac { c _ { 1 } } { c _ { 2 } }$
$\therefore$The pair of equations has infinitely many solutions.

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 "2 Marks Questions" from Pair of Linear Equations in Two Variables→Pair of Linear Equations in Two Variables — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

A lot of $20$ bulbs contain $4$ defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
Suppose the bulb drawn in $(i)$ is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

What is the probability that a leap year has $53$ Sundays and $53$ Mondays$?$

Find the length of the altitude of an equilateral triangle of side $2a\ cm.$

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{35}{50}$

Harpreet tosses two different coins simultaneously $($say, one is of Re $1$ and other of $Rs. 2).$ What is the probability that he gets at least one head$?$

Find the coordinates of the point of trisection (i.e., points dividing in three equal parts) of the line segment joining the points $A(2, – 2)$ and $B(–7, 4)$.

A path of $8m$ width runs around the outside of a circular park whose radius is $17m$. Find the area of the path.$\Big[\text{Use }\pi=\frac{22}{7}\Big]$

Very-Short-Answer Question:
If one zero of the polynomial $x^2- 4x + 1$ is $2+\sqrt3.$ Write the other zero.

The angle of elevation of the top of a tower from a point on the ground, which is $30\ m$ away from the foot of the tower, is $30^\circ$. Find the height of the tower.

Very-Short and Short-Answer Questions:
If $\sin\theta=\text{x},$ write the value of $\cot\theta.$