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

There are $40$ students in class $X$ of a school of whom $25$ are girls and $15$ are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of

a girl?
a boy?

Is the given statement correct or not correct?
If two coins are tossed simultaneously there are three possible outcomes- two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$.

A point $P$ is $26\ cm$ away from the centre $O$ of a circle and the length $PT$ of the tangent drawn from $P$ to the circle is $10\ cm.$ Find the radius of the circle.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be $55$ minus the number of toys produced in a day. On a particular day, the total cost of production was $₹ 750$. We would like to find out the number of toys produced on that day. Represent the situations mathematically (quadratic equation).

In an $AP$: $a = 3, n = 8, s = 192$, find $d$.

In $\triangle$$PQR$, right-angled at $Q, PQ = 3\ cm$ and $PR = 6\ cm$. Determine $\angle$$QPR$ and $\angle$$PRQ$.

E and F are points on the sides PQ and PR respectively of a $\triangle$PQR. For PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm case, state whether EF || QR.

What is the value of $\sin^2\theta+\frac{1}{1+\tan^2\theta}?$

Prove the following trigonometric identities.
$\frac{1-\sin\theta}{1+\sin\theta}=(\sec\theta-\tan\theta)^2$

Show that the progressions given below is an $AP$. Find the first term, common difference and next term.
$11, 6, 1, -4, ....$