SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Pair of Linear Equations in Two Variables

12 questions · 12 still being checked

EXERCISE 3.3 1–2 (part 3 of 3)

  1. Exercise 1

    Solve the following pair of linear equations by the elimination method and the substitution method:
    (i)
    x+y=5\displaystyle x+y=5 and 2x−3y=4\displaystyle 2 x-3 y=4
    (ii)
    3x+4y=10\displaystyle 3 x+4 y=10 and 2x−2y=2\displaystyle 2 x-2 y=2
    (iii)
    3x−5y−4=0\displaystyle 3 x-5 y-4=0 and 9x=2y+7\displaystyle 9 x=2 y+7
    (iv)
    x2+2y3=−1\displaystyle \frac{x}{2}+\frac{2 y}{3}=-1 and x−y3=3\displaystyle x-\frac{y}{3}=3
    NCERT’s answer
    (i)
    $\displaystyle x=\frac{19}{5}, y=\frac{6}{5}$ (ii) $\displaystyle x=2, y=1$ (iii) $\displaystyle x=\frac{9}{13}, y=-\frac{5}{13}$ (iv) $\displaystyle x=2, y=-3$

    Working being prepared

  2. Exercise 2

    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :
    (i)
    If we add 1\displaystyle 1 to the numerator and subtract 1\displaystyle 1 from the denominator, a fraction reduces to 1\displaystyle 1 . It becomes 12\displaystyle \frac{1}{2} if we only add 1\displaystyle 1 to the denominator. What is the fraction?
    (ii)
    Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
    (iii)
    The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
    (iv)
    Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50\displaystyle 50 and ₹ 100\displaystyle 100 notes only. Meena got 25\displaystyle 25 notes in all. Find how many notes of ₹ 50\displaystyle 50 and ₹ 100\displaystyle 100 she received.
    (v)
    A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27\displaystyle 27 for a book kept for seven days, while Susy paid ₹ 21\displaystyle 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
    NCERT’s answer
    (i)
    $\displaystyle x-y+2=0,2 x-y-1=0$, where $\displaystyle x$ and $\displaystyle y$ are the numerator and denominator of the fraction; $\displaystyle \frac{3}{5}$. (ii) $\displaystyle x-3 y+10=0, x-2 y-10=0$, where $\displaystyle x$ and $\displaystyle y$ are the ages (in years) of Nuri and Sonu respectively. Age of Nuri $\displaystyle (x)=50$, Age of Sonu $\displaystyle (y)=20$. (iii) $\displaystyle x+y=9,8 x-y=0$, where $\displaystyle x$ and $\displaystyle y$ are respectively the tens and units digits of the number; 18. (iv) $\displaystyle x+2 y=40, x+y=25$, where $\displaystyle x$ and $\displaystyle y$ are respectively the number of ₹ $\displaystyle 50$ and ₹ $\displaystyle 100$ notes; $\displaystyle x=10, y=15$. (v) $\displaystyle x+4 y=27, x+2 y=21$, where $\displaystyle x$ is the fixed charge (in ₹) and $\displaystyle y$ is the additional charge (in ₹) per day; $\displaystyle x=15, y=3$.

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