 # Worksheets for Linear equations in two variable

Given below are the linear equations in two variables class 10 worksheet with solutions

Question 1.
Solve these linear equation in two variable ( x and y)
a. $37x + 41y = 70$
$41x + 37y = 86$

b. $99x + 101y = 499$
$101x + 99y = 501$

c. $23x - 29y = 98$
$29x - 23y =110$

d. $ax + by = a - b$
$bx - ay = a + b$

e. $x + y = a + b$
$ax - by = a^2 - b^2$

f. $(a - b) x + (a + b) y = a^2 - 2ab - b^2$
$(a + b) (x + y) = a^2 - b^2$

g. $8x - 3y = 5xy$
$5y = -2xy$

h. $3(2x + y) = 7xy$
$3(x + 3y) = 11xy$

i. $49x + 51y = 499$
$51x + 49y = 501$

j. $217x + 131y = 913$
$131x + 217y = 827$

Qustion 2
Solve these linear equation in two variable ( x and y)
i. $\frac {1}{2x} + \frac {1}{3y} = 2$
$\frac {1}{3x} + \frac {1}{2y} = \frac {13}{6}$

ii) $\frac {2}{x} + \frac {3}{y} = \frac {9}{xy}$
$\frac {4}{x} + \frac {9}{y} = \frac {21}{xy}$
Where $x \ne 0,y \ne 0$

iii. $\frac {22}{x+y} + \frac {15}{x-y} = 5$
$\frac {55}{x+y} + \frac {45}{x-y} = 14$

iv.$\frac {5}{x+y} - \frac {2}{x-y} = -1$
$\frac {15}{x+y} + \frac {7}{x-y} = 10$

v. $bx + cy=a+b$
$ax( \frac {1}{a-b} - \frac {1}{a+b}) + cy ( \frac {1}{b-a} - \frac {1}{b+a})= \frac {2a}{a+b}$

vi)$\frac {1}{2(2x+3y)} + \frac {1}{7(3x-2y)} = \frac {17}{20}$
$\frac {7}{(2x+3y)} - \frac {1}{(3x-2y)} = -\frac {28}{5}$

vii.$\frac {x+1}{2} - \frac {y +4}{11} = 2$
$\frac {x+3}{2} + \frac {2y+3}{17} = 5$

viii.$\frac {7x -2y}{xy} =5$
$\frac {8x+7y}{xy} =15$

ix. $\frac {x}{a} + \frac {y}{b} =2$
$ax -by = a^2 - b^2$

x.$\frac {57}{x+y} + \frac {6}{x-y} = 5$
$\frac {38}{x+y} + \frac {21}{x-y} = 9$

Question 3.
In a cyclic quadrilateral ABCD,Find the four angles.
a. $\angle A = (2x + 4)$, $\angle B = (y + 3)$, $\angle C = (2y + 10)$, $\angle D = (4x -5)$.
b. $\angle A = (2x - 1)$, $\angle B = (y + 5)$, $\angle C = (2y + 15)$ and $\angle D = (4x -7)$

Question 4.
Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs:
$3x - 2y = 4$
$6x + 2y = 4$
$9x -6y = 12$

Question 5
Find the values of a and b for which the following system of linear equations has infinite number of solutions:
$2x + 3y = 7$
$2ax + (a + b)y = 28$

Question 6
Find the values of a and b for which the following system of linear equations has infinite number of solutions:
$2x -3y = 7$
$(a + b)x - (a + b- 3)y = 4a + b$

Question 7.
In a ABC, $\angle A = x$, $\angle B = (3x -2)$, $\angle C = y$ Also $\angle C - \angle B = 9$. Find the three angles.

Question 8.
Find the value of k for which the system of equations x + 2y -3 = 0 and ky + 5x + 7 = 0 has a unique solution.

Question 9
For what value of a the system of linear equations $2x + 3y = 7$ and $(a -1)x + (a + 1)y = 3a - 1$ represent parallel lines.

Question 10
If the lines $x + 2y + 7 = 0$ and $2x + ky + 18 = 0$ intersect at a point, then find the value of k.

Question 11
Is $x = 5, y = -5$ a solution of the linear equation $3x + 2y - 5 = 0$?

Question 12.
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. Find the present ages of the son and the father.

## Summary

This linear equations in two variables worksheet class 10 with solutions 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. Go back to Class 10 Main Page using below links

### 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