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Graphical Questions for Linear equations in Two Variable





Given below are the linear equations in two variables class 10 graph questions with amswers. These are important questions for the examination
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Question 1.
Draw the graphs of the following equations:
$2x - y - 2 = 0$
$4x + 3y - 24 = 0$
$y + 4 = 0$
Obtain the vertices of the triangle so obtained. Also, determine its area.

Answer

We can draw the graph as shown in below figure
Class 10 Maths Graphical Questions for Linear equations in two variables
Vertices of the triangle so obtained are (3,4) , (-1,-4) and (9,-4)
Area of the Triangle ABC can be calculated using
$=\frac {1}{2} Base \times Height$
$=\frac {1}{2} \times 8 \times 10= 40$


Question 2.
Determine graphically the vertices of the triangles, the equations of whose sides are given below:
(i) $2y - x = 8$, $5y - x = 14$ and $y - 2x = 1$
(ii) $y = x$,$y = 0$ and $3x + 3y = 10$

Answer

(i)
linear equations in two variables graph questions
Vertices of the triangle so obtained are (-4, 2) (1, 3) (2, 5)
(ii)

(0, 0) (10/3, 0) (5/3, 5/3)


Question 3.
Solve the following system of linear equations graphically:
$3x + y - 11 = 0$, $x - y - 1 = 0$
Shade the region bounded by these lines and y - axis. Also, find the area of the region bounded by the these lines and y - axis.

Answer


Lines intersect at (3,2)
Area of Triangle ABC
$=\frac {1}{2} \times 12 \times 3=18$ sq units


Question 4.
Solve:
x + 2y + z = 7
x + 3z = 11
2x - 3y = 1

Answer

Answer x = 2, y = 1, z = 3


Question 5.
Solve graphically the pair of linear equations:
$3x - 4y + 3 = 0$ and $3x + 4y - 21 = 0$
Find the coordinates of the vertices of triangular region formed by these lines and x- axis. Also, calculate the area of this triangle.

Answer

graph of linear equations in two variables class 10
Vertices of the triangle so obtained are (-1,0) ,(3,3) and (7,0)
Area of Triangle
$=\frac {1}{2} B \times H= \frac {1}{2} \times 8 \times 3=12$ sq units


Question 6.
Solve the following system of linear equations graphically:
$x - y = 1$
$2x + y = 8$
Shade the area bounded by these two lines and y - axis. Also, determine this area.

Answer


The lines intersect at (3,2)
Area of the triangle
$=\frac {1}{2}B \times H = \frac {1}{2} \times 9 \times 3= 13.5$ sq units


Question 7.
Draw the graphs of the following equations on the same graph paper.
$2x + 3y = 12$
$x - y = 1$
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y- axis.

Answer


The coordinates of the vertices of the triangle formed by the two straight lines and the y- axis 3,2


Question 8.
Draw the graphs of x - y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and x- axis and shade the triangular area. Calculate the area bounded by these lines and x- axis.

Answer


The coordinates of the vertices of the triangle formed by these lines and x- axis are (-1,0) ,(2,3) and (4,0)
Area of the triangle
$=\frac {1}{2}B \times H = \frac {1}{2} \times 5 \times 3= 7.5$ sq units


Question 9.
Solve the following system of linear equations graphically and find the vertices of the triangle formed by these lines and x - axis:
$x - y - 1 = 0$ ,$x + 1 = 0$

Question 10.
Solve the following pair of equations graphically:
$3x - y = 7$, $2x + 5y + 1 = 0$

Answer


Question 11.
Draw the graph of the following pair of linear equations:
3x + 2y = 15 and 3x - 4y = -3
Also, shade the region bounded by these lines and y = 0. Write the coordinated vertices of the triangle.
Question 12.
Solve graphically the pair of linear equations:
3x - 2y + 7 = 0; 2x + 3y - 4 = 0
Question 13.
Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m - 1) x + 3y - 5 = 0
3x + (n - 1) y - 2 = 0
Question 14.
Solve the following system of linear equations graphically and find the vertices of the triangle formed by these lines and x - axis:
x - y - 1 = 0; x + 1 = 0

Summary

This graph questions for class 10 linear equations in two variables with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.



Also Read




Go back to Class 10 Main Page using below links
Class 10 Maths Class 10 Science

Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20



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