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NCERT Exemplar · Class 9 Mathematics Linear Equations in Two Variables

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EXERCISE 4.2 1–7 (part 3 of 5)

  1. Write whether the following statements are True or False? Justify your answers :

    Exercise 1

    The point (0,3)\displaystyle (0,3) lies on the graph of the linear equation 3x+4y=12\displaystyle 3 x+4 y=12.

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    NCERT’s answer
    True, since $\displaystyle (0,3)$ satisfies the equation $\displaystyle 3 x+4 y=12$.
    TrueSubstitute the point into the equation: \[3(0)+4(3)=12 \] \[12=12 \] The coordinates satisfy \(\displaystyle 3x+4y=12\), so \(\displaystyle (0,3)\) lies on its graph.

  2. Exercise 2

    The graph of the linear equation x+2y=7\displaystyle x+2 y=7 passes through the point (0,7)\displaystyle ( 0,7 ).

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    NCERT’s answer
    False, since $\displaystyle (0,7)$ does not satisfy the equation.
    FalseSubstitute \(\displaystyle x=0,\ y=7\): \[0+2(7)=14 \] Since \(\displaystyle 14\neq 7\), the point \(\displaystyle (0,7)\) does not satisfy \(\displaystyle x+2y=7\), so the graph does not pass through it.

  3. Exercise 3

    The graph given below represents the linear equation x+y=0\displaystyle x+y=0.

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    NCERT’s answer
    True, since $\displaystyle (-1,1)$ and $\displaystyle (-3, 3)$ satisfy the given equation and two points determine a unique line.
    True NCERT_Solution_Class9_Maths_Exemplar_Ch4_Ex4-2_Q3 \[(-3)+3=0,\qquad (-1)+1=0 \] Both points marked on the graph satisfy \(\displaystyle x+y=0\); since two points determine a unique line, the line shown is the graph of \(\displaystyle x+y=0\).

  4. Exercise 4

    The graph given below represents the linear equation x=3\displaystyle x=3 (see Fig. 4.2\displaystyle 4.2). NCERT_Question_Class9_Maths_Exemplar_Ch4_Ex4-2_Q4

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    NCERT’s answer
    True, since this graph is a line parallel to $\displaystyle y$-axis at a distance $\displaystyle 3$ units (to the right) from it.
    TrueNCERT_Solution_Class9_Maths_Exemplar_Ch4_Ex4-2_Q4The drawn line is vertical through \(\displaystyle (3,0)\): every point on it has \[x=3,\quad y\in\mathbb{R} \] which is exactly the solution set of \(\displaystyle x=3\).

  5. Exercise 5

    The coordinates of points in the table:
    x\displaystyle x0\displaystyle 01\displaystyle 12\displaystyle 23\displaystyle 34\displaystyle 4
    y\displaystyle y2\displaystyle 23\displaystyle 34\displaystyle 4-5\displaystyle 56\displaystyle 6
    represent some of the solutions of the equation x−y+2=0\displaystyle x-y+2=0.

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    NCERT’s answer
    False, since the point $\displaystyle (3,-5)$ does not satisfy the given equation.
    False\[x-y+2=0 \]Four pairs satisfy it: \[(0,2),\ (1,3),\ (2,4),\ (4,6) \]The fifth does not: \[3-(-5)+2=10\neq 0 \]\(\displaystyle (3,-5)\) fails the equation, so the table is not entirely made of solutions.

  6. Exercise 6

    Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

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    NCERT’s answer
    False, since every point on the graph of the equation represents a solution.
    False\[ax+by+c=0 \]The graph is the set of points \(\displaystyle (x,y)\) satisfying this equation, so every point plotted on it is automatically a solution.

  7. Exercise 7

    The graph of every linear equation in two variables need not be a line.

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    NCERT’s answer
    False, since the graph of a linear equation in two variables is always a line.
    False \[ax+by+c=0 \implies y=-\frac{a}{b}x-\frac{c}{b}\quad(b\neq0) \] This is linear in \(\displaystyle x\), so its graph is a straight line. \[b=0 \implies x=-\frac{c}{a}\quad\text{(a vertical line)} \] Either way the graph is always a line, never a curve.