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Chapter 4: Linear Equations in Two Variables

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This page provides comprehensive Chapter 4: Linear Equations in Two Variables - Standard Worksheet - SJMaths. Standard level practice worksheet for Class 9 Linear Equations in Two Variables.

Standard Level Worksheet

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  1. Question 1: Find the value of $k$, if $x = 2, y = 1$ is a solution of the equation $2x + 3y = k$.
    Solution: Substitute $x=2, y=1$ in the equation: $2(2) + 3(1) = k \Rightarrow 4 + 3 = k \Rightarrow k = 7$.
  2. Question 2: The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
    Solution: Let cost of notebook be $x$ and pen be $y$.
    According to condition: $x = 2y \Rightarrow x - 2y = 0$.
  3. Question 3: Find the coordinates of the point where the graph of the equation $3x + 4y = 12$ cuts the x-axis.
    Solution: On x-axis, $y = 0$.
    $3x + 4(0) = 12 \Rightarrow 3x = 12 \Rightarrow x = 4$.
    The point is $(4, 0)$.
  4. Question 4: If the point $(3, 4)$ lies on the graph of the equation $3y = ax + 7$, find the value of $a$.
    Solution: Substitute $x=3, y=4$:
    $3(4) = a(3) + 7 \Rightarrow 12 = 3a + 7 \Rightarrow 3a = 5 \Rightarrow a = 5/3$.
  5. Question 5: Give the geometric representation of $2x + 9 = 0$ as an equation in two variables.
    Solution: In two variables, it is $2x + 0y + 9 = 0$. The graph is a straight line parallel to the y-axis passing through $x = -4.5$.
  6. Question 6: Write two solutions for the equation $4x + 3y = 12$.
    Solution: 1) Let $x=0 \Rightarrow 3y=12 \Rightarrow y=4$. Sol: $(0, 4)$.
    2) Let $y=0 \Rightarrow 4x=12 \Rightarrow x=3$. Sol: $(3, 0)$.
  7. Question 7: At what point does the graph of the linear equation $x + y = 5$ meet a line which is parallel to the y-axis, at a distance 2 units from the origin and in the positive direction of x-axis?
    Solution: Line parallel to y-axis at distance 2 is $x = 2$.
    Put $x=2$ in $x+y=5 \Rightarrow 2+y=5 \Rightarrow y=3$.
    Point is $(2, 3)$.
  8. Question 8: If the temperature is $95^\circ F$, what is the temperature in Celsius? (Use $F = \frac{9}{5}C + 32$)
    Solution: $95 = \frac{9}{5}C + 32 \Rightarrow 95 - 32 = \frac{9}{5}C \Rightarrow 63 = \frac{9}{5}C \Rightarrow C = \frac{63 \times 5}{9} = 35^\circ C$.
  9. Question 9: Does the graph of the linear equation $y = x + 2$ pass through the origin?
    Solution: At origin, $x=0, y=0$.
    Substitute in equation: $0 = 0 + 2 \Rightarrow 0 = 2$, which is false. So, it does not pass through the origin.
  10. Question 10: Find the area of the triangle formed by the line $2x + 3y = 6$ and the coordinate axes.
    Solution: x-intercept (put $y=0$): $x=3$. y-intercept (put $x=0$): $y=2$.
    Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 2 = 3$ sq units.
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