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NCERT Solutions · Class 9 Mathematics Two Variables, One Line

42 questions · 42 still being checked

Exercise Set 13.1 1–3 (part 1 of 7)

  1. Exercise 1

    Write a linear equation in two variables in which a=3,b=0\displaystyle a=3, b=0 and c=−15\displaystyle c=-\frac{1}{5}.

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    Put \(\displaystyle a=3,\ b=0,\ c=-\tfrac15 \) in \(\displaystyle ax+by+c=0 \):\[3x+0\cdot y-\tfrac15=0 \]\[3x-\tfrac15=0 \]Answer: \(\displaystyle 3x+0\cdot y-\tfrac15=0 \)

  2. Exercise 2

    Complete the following table after expressing the given linear equations in standard form.
    Linear equation in two variablesStandard FormCoefficient of x\displaystyle \boldsymbol{x}Coefficient of y\displaystyle yConstant term
    y−15=2x\displaystyle y-15=\sqrt{2} x
    3y−2x=0\displaystyle 3 y-2 x=0
    5x=3y\displaystyle 5 x=3 y
    x=8\displaystyle x=8
    3y=1\displaystyle 3 y=1

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    This solution has not been cross-checked against the answer printed in NCERT.

    Move every term to the left-hand side to get \(\displaystyle ax+by+c=0 \):\[y-15=\sqrt2\,x \;\Rightarrow\; -\sqrt2\,x+y-15=0 \]\[3y-2x=0 \;\Rightarrow\; -2x+3y+0=0 \]\[5x=3y \;\Rightarrow\; 5x-3y+0=0 \]\[x=8 \;\Rightarrow\; x+0\cdot y-8=0 \]\[3y=1 \;\Rightarrow\; 0\cdot x+3y-1=0 \]\[\begin{array}{|l|l|c|c|c|} \hline \text{Equation} & \text{Standard form} & a & b & c \\ \hline y-15=\sqrt2\,x & -\sqrt2\,x+y-15=0 & -\sqrt2 & 1 & -15 \\ \hline 3y-2x=0 & -2x+3y+0=0 & -2 & 3 & 0 \\ \hline 5x=3y & 5x-3y+0=0 & 5 & -3 & 0 \\ \hline x=8 & x+0\cdot y-8=0 & 1 & 0 & -8 \\ \hline 3y=1 & 0\cdot x+3y-1=0 & 0 & 3 & -1 \\ \hline \end{array} \]Multiplying a row by \(\displaystyle -1 \) gives an equally valid standard form.Answer: the table above, with \(\displaystyle (a,b,c)=(-\sqrt2,1,-15),\ (-2,3,0),\ (5,-3,0),\ (1,0,-8),\ (0,3,-1) \)

  3. Exercise 3

    (i)
    The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹ t\displaystyle t and that of a pen to be ₹ p\displaystyle p. Charlie wrote t=2p\displaystyle t=2 p, whereas Meera wrote p=2t\displaystyle p=2 t. Which of these two representations is correct?
    (ii)
    In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176\displaystyle 176 runs. Manisha expressed this situation as x+y=176\displaystyle x+y=176, where the number of runs scored by one batsman is x\displaystyle x, and the number of runs scored by the other is y\displaystyle y. Is this a correct representation?

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    (i) The notebook costs twice the pen:\[t=2\times p=2p \]Meera's \(\displaystyle p=2t \) makes the pen cost twice the notebook. Test with pen ₹$\displaystyle 5$, notebook ₹$\displaystyle 10$:\[t=2p:\quad 10=2\times5 \]\[p=2t:\quad 5\neq 2\times10=20 \](ii) Together the two batsmen scored $\displaystyle 176$ runs:\[x+y=176 \]So Manisha's representation is correct.Answer: (i) Charlie's \(\displaystyle t=2p \) is correct; (ii) yes, \(\displaystyle x+y=176 \) is correct