Chapter 3 · Pair of Linear Equations

NCERT Class 10 Maths Exercise 3.2

All 3 questions of NCERT Class 10 Maths Exercise 3.2 (Pair of Linear Equations), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Solve ​the following pair of linear ​equations ​by the substitution method: ​

   1. (i)$x+y=14$ ​and $x-y=4$
   2. (ii)$s-t=3$ and $\frac{s}{3}+\frac{t}{2}=6$ ​
   3. (iii)$3x-y=3$ and $9x-3y=9$
   4. (iv)$0.2x+0.3y=1.3$ ​and $0.4x+0.5y=2.3$
   5. (v)$\sqrt{2}x+\sqrt{3}y=0$ and $\sqrt{3}x-\sqrt{8}y=0$
   6. (vi)$\frac{3x}{2}-\frac{5y}{3}=-2$ and $\frac{x}{3}+\frac{y}{2}=\frac{13}{6}$
   Show answer

   (i) $x=9,y=5$; (ii) $s=9,t=6$; (iii) Infinitely many solutions ($y=3x-3$); (iv) $x=2,y=3$; (v) $x=0,y=0$; (vi) $x=2,y=3$.

   Step-by-step solution →
2. Q2
   Solve $2x+3y=11$ and $2x-4y=-24$ ​and ​hence ​find the ​value of ​'$m$' ​for which $y=mx+3$.
   Show answer

   $x=-2,y=5$, and $m=-1$.

   Step-by-step solution →
3. Q3
   Form the pair of linear equations for the following problems ​and find their solution by the substitution method:

   1. (i)The difference between two numbers is $26$ and one number is three times the ​other. Find them.
   2. (ii)The larger of two supplementary ​angles exceeds the smaller by $18$ degrees. Find them.
   3. (iii)The coach of a cricket team buys $7$ bats and $6$ balls for Rs $3800$. Later, she buys $3$ bats and $5$ balls for Rs $1750$. Find the cost of each bat and each ​ball.
   4. (iv)The taxi ​charges in a city consist of a fixed charge together with the charge ​for the distance covered. For a distance of $10$ km, the charge paid is Rs $105$ and ​for a journey of $15$ km, the charge paid is Rs $155$. What are the fixed charges and the charge per km? How much does a person ​have to pay for travelling a distance of $25$ km?
   5. (v)A fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator. If $3$ is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
   6. (vi)Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?
   Show answer

   (i) 39 and 13; (ii) $99^{\circ }$ and $81^{\circ }$; (iii) bat Rs 500, ball Rs 50; (iv) fixed Rs 5, Rs 10 per km, Rs 255 for 25 km; (v) $7/9$; (vi) Jacob is 40 and his son is 10.

   Step-by-step solution →