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Mathematics · Pair of Linear Equations in Two Variables · NCERT Exercises

Exercise 3.2

Complete, independently verified solutions for NCERT Exercise 3.2.

Mathematics · Chapter 3 · NCERT Exercises

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Question 1

substitution method

Solve by substitution.

  1. x+y=14; x−y=4x+y=14;\ x-y=4
  2. s−t=3; s3+t2=6s-t=3;\ \frac{s}{3}+\frac{t}{2}=6
  3. 3x−y=3; 9x−3y=93x-y=3;\ 9x-3y=9
  4. 0.2x+0.3y=1.3; 0.4x+0.5y=2.30.2x+0.3y=1.3;\ 0.4x+0.5y=2.3
  5. 2x3+3y=0; 3x−8y=0\frac{2x}{3}+3y=0;\ 3x-8y=0
  6. 3x2−5y3=−2; x3+y2=136\frac{3x}{2}-\frac{5y}{3}=-2;\ \frac{x}{3}+\frac{y}{2}=\frac{13}{6}

Solution

  1. x=14−y⇒14−2y=4⇒(x,y)=(9,5)x=14-y\Rightarrow14-2y=4\Rightarrow(x,y)=(9,5)
  2. s=t+3; 2s+3t=36⇒(s,t)=(9,6)s=t+3;\ 2s+3t=36\Rightarrow(s,t)=(9,6)

  3. The second equation is three times the first: infinitely many solutions.

  4. 2x+3y=13, 4x+5y=23⇒(x,y)=(2,3)2x+3y=13,\ 4x+5y=23\Rightarrow(x,y)=(2,3)
  5. x=8y3⇒43y9=0⇒(x,y)=(0,0)x=\frac{8y}{3}\Rightarrow\frac{43y}{9}=0\Rightarrow(x,y)=(0,0)
  6. 9x−10y=−12, 2x+3y=13⇒(x,y)=(2,3)9x-10y=-12,\ 2x+3y=13\Rightarrow(x,y)=(2,3)

Question

Question 2

substitution method

Solve 2x + 3y = 11 and 2x − 4y = −24; hence find m if y = mx + 3.

Solution

7y=35⇒y=5,x=−27y=35\Rightarrow y=5,\qquad x=-2
5=−2m+3⇒m=−15=-2m+3\Rightarrow m=-1

Both original equations evaluate correctly.

Final answer

x=−2,y=5,m=−1x=-2,\quad y=5,\quad m=-1

Question

Question 3

substitution method · word problems

Form equations and solve by substitution.

  1. Two numbers differ by 26; one is three times the other.

  2. Supplementary angles differ by 18°.

  3. 7 bats and 6 balls cost ₹3800; 3 bats and 5 balls cost ₹1750.

  4. Taxi fares are ₹105 for 10 km and ₹155 for 15 km. Find fixed and per-km charges and the 25 km fare.

  5. A fraction becomes 9/11 after adding 2 to numerator and denominator, and 5/6 after adding 3.

  6. Five years hence Jacob is three times his son; five years ago he was seven times his son.

Solution

  1. x−y=26, x=3y⇒(x,y)=(39,13)x-y=26,\ x=3y\Rightarrow(x,y)=(39,13)
  2. L+S=180, L−S=18⇒(L,S)=(99∘,81∘)L+S=180,\ L-S=18\Rightarrow(L,S)=(99^\circ,81^\circ)
  3. 7b+6c=3800, 3b+5c=1750⇒(b,c)=(500,50)7b+6c=3800,\ 3b+5c=1750\Rightarrow(b,c)=(500,50)
  4. f+10r=105, f+15r=155⇒(f,r)=(5,10)f+10r=105,\ f+15r=155\Rightarrow(f,r)=(5,10)
    f+25r=255f+25r=255
  5. 11x−9y=−4, 6x−5y=−3⇒(x,y)=(7,9)11x-9y=-4,\ 6x-5y=-3\Rightarrow(x,y)=(7,9)
  6. J−3S=10, J−7S=−30⇒(J,S)=(40,10)J-3S=10,\ J-7S=-30\Rightarrow(J,S)=(40,10)

Final answer

Answers: 39 and 13; 99° and 81°; ₹500 and ₹50; ₹5 fixed, ₹10/km, ₹255; 7/9; 40 and 10 years.