Chapter 13 Linear Equations in Two Variables RD Sharma Solutions Exercise 13.4 Class 9 Maths
Chapter Name  RD Sharma Chapter 13 Linear Equations in Two Variables Exercise 13.4 
Book Name  RD Sharma Mathematics for Class 10 
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Related Study  NCERT Solutions for Class 10 Maths 
Exercise 13.4 Solutions
1. Given the geometric representations of the following equations
(a) on the number line
(b) on the Cartesian plane :
(i) x = 2
(ii) y + 3 = 0
(iii) y = 3
(iv) 2x+ 9 = 0
(v) 3x  5 = 0
Solution
x = 2Point A represents x = 2 number line
On Cartesian plane, equation represents all points on y  axis for which x = 2
(ii)
y = 3
Point A represents 3 on number line
y = 3
Point A represents 3 on number line
On Cartesian plane, equation represents all the points on x  axis for which y = 3 .
(iii)
y = 3.
Point A represents 3 on number line
On Cartesian plane, equation represents all points all points on x  axis for which y = 3
2x + 9 = 0
2x = 9
x = 9/2 = 4.5
Point A represents 4.5 on number line
2x = 9
x = 9/2 = 4.5
Point A represents 4.5 on number line
On Cartesian plane, equation represents all points on y  axis for which x = 4.5
(v)
3x  5 = 0 3x = 5
x = 5/3 = 1.6 (Approx)
Point A represents 1(1/2) or 5/3 on number line
On Cartesian plane, equation represents all points on y  axis for which x = 16
2. Give the geometrical representation of 2x + 13 = 0 as an equation in
(i) one variable
(i) one variable
(ii) two variable
Solution
Solution
(i)
One variable representation of 2x + 13 = 0
2x = 13
x = 13/2 = 6(1/2)
Points A represents 13/2
2x = 13
x = 13/2 = 6(1/2)
Points A represents 13/2
(ii)
Two variable representation of 2x + 13 = 0 2x + 0y + 13 = 0
⇒ 2x + 13 = 0
⇒ 2x =  13
⇒ x = 13/2
⇒ x = 6.5
On Cartesian plane, equation represents all points y  axis for which x = 6.5.
3. Solve the equation 3x + 2 = x  8, and represent the solution (i) the number line (ii) the Cartesian plane.
Solution
(i)
3x + 2 = x  8 ⇒ 3x  x = 8  2
⇒ 2x = 10
⇒ x = 5
Points A represents 5 on number line
On Cartesian plane, equation represents all points on y  axis for which x = 5
4. Write the equation of the line that is parallel to x  axis and passing through the point
(i) (0, 3)
(ii) (0, 4)
(iii) (2, 5)
(iv) (4,  3)
Solution
Solution
(i) The equation of the line that is parallel to x  axis and passing through the point (0, 3) is y = 3
(ii) The equation of the line that is parallel to x  axis and passing through the point (0, 4) is y = 4
(iii) The equation of the line that is parallel to x  axis and passing through the point (2, 5) is y = 5
(iv) The equation of the line that is parallel to x  axis and passing through the point (4,  3) is y = 3
(ii) The equation of the line that is parallel to x  axis and passing through the point (0, 4) is y = 4
(iii) The equation of the line that is parallel to x  axis and passing through the point (2, 5) is y = 5
(iv) The equation of the line that is parallel to x  axis and passing through the point (4,  3) is y = 3
5. Write the equation of the line that is parallel to y  axis and passing through the point
(i) (4, 0)
(ii) (2, 0)
(iii) (3, 5)
(iv) (4, 3)
Solution
(i) The equation of the line that is parallel to y  axis and passing through (4, 0) will be x = 4
(ii) The equation of the line that is parallel to y  axis and passing through (2, 0) will be x = 2
(iii) The equation of the line that is parallel to y  axis and passing through (3, 5) will be x = 3
(iv) The equation of the line that is parallel to y axis and passing through (4, 3) will be x = 4.
(ii) The equation of the line that is parallel to y  axis and passing through (2, 0) will be x = 2
(iii) The equation of the line that is parallel to y  axis and passing through (3, 5) will be x = 3
(iv) The equation of the line that is parallel to y axis and passing through (4, 3) will be x = 4.