 # Worksheets for Linear equations in two variable

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

1.
i. (3, 2)
ii. (3, -1)
iii. (8, 3)
iv. (1,-1)
v. (a, b)
vi. (a,-b)
vii. (0, 0) ,(22/31, 11/23)
viii. (0,0) (1,3/2)
ix. (1 ½ , 9/2)
x. 3,2

2.
i. (1/2, 1/3)
Hint: Take $\frac {1}{6x}=p , \frac {1}{6y} =q$ and then solve in p& q and then find x and y

ii. (1 ,3)
Hint: Take $\frac {1}{x}=p , \frac {1}{y} =q$ and then solve in p& q and then find x and y

iii. (8,3)
Hint: Take $\frac {1}{x+y}=p , \frac {1}{x-y} =q$ and then solve in p& q and then find x and y

iv. (3,2)
Hint: Take $\frac {1}{x+y}=p , \frac {1}{x-y} =q$ and then solve in p& q and then find x and y

v. $\frac {a}{b},\frac {b}{c}$ vi. (2,1)
Hint: Take $\frac {1}{2x+3y}=p , \frac {1}{3x-2y} =q$ and then solve in p& q and then find x and y

vii. 5, 7
viii. (1, 1)
Hint:
Convert into these forms
$\frac {7}{y} - \frac {2}{x} =5$
$\frac {8}{y} + \frac {7}{y} =15$
Take $\frac {1}{x}=p , \frac {1}{y} =q$ and then solve in p& q and then find x and y

ix. (a,b)
x. (11, 8)

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### 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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