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}$

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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