Worksheets for Linear equations in two variable Class 10

 

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

Answer

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)