Question 1 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<br/>$6x - ay = 8$<br/>In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$

Question 2 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be

Question 4 :
The&#160;&#160;linear equation, such that each point on its graph has an ordinate $3$ times its abscissa is $y=mx$. Then the value of&#160;$m$ is<br/>

Question 6 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.

Question 7 :
A line which passes through (5, 6) and (-3. -4) has an equation of

Question 8 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point

Question 9 :
What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point ?

Question 10 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at&#160;

Question 12 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.

Question 13 :
Examine whether the&#160;point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.

Question 14 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$&#160;has a non-zero solution, is ________.

Question 15 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is

Question 16 :
Find the value of x and y using cross multiplication method: <br/>$x-&#160; 2y = 1$ and $x + 4y = 6$

Question 17 :
Solve the following pair of simultaneous equations:$\displaystyle\, 4x\, +\, \frac{3}{y}\, =\, 1\,; 3x\, -\, \frac{2}{y}\, =\, 5$

Question 18 :
Solve the following pair of equations :$x\, -\, y\, =\, 0.9$<br/>$\displaystyle \frac{11}{2\, (x\, +\, y)}\, =\, 1$

Question 19 :
Find the value of x and y using elimination method:<br/>$\dfrac{-1}{x} + \dfrac{2}{y} = 0$ and $\dfrac{x}{2}+&#160; \dfrac{y}{3} = 1$<br/>

Question 20 :
If $2x=t+\sqrt{t^2+4}$ and $3y=t-\sqrt{t^2+4}$ then the value of&#160; $y$ when $x=\dfrac {2}{3}$, is ____.

Question 21 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:&#160;$2x - 3y= 7$, $5x + y &#160;=9$

Question 22 :
If $y=a+\dfrac { b }{ x } $, where $a$ and $b$ are constants and if $y=1$ when $x=-1$, and $y=5$ when $x=-5$, what is the value of $a+b$?

Question 23 :
The simultaneous equations,&#160;$\displaystyle y = x + 2|x| $ &amp; $y = 4 + x - |x|$ have the solution set&#160;

Question 24 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {1}{(x-1)}+\dfrac {1}{(y-2)}=2, \ \dfrac {6}{(x-1)}-\dfrac {2}{(y-2)}=1$<br/>

Question 25 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$

Question 26 :
Equations $\displaystyle \left ( b-c \right )x+\left ( c-a \right )y+\left ( a-b \right )=0$ and $\displaystyle \left ( b^{3}-c^{3} \right )x+\left ( c^{3}-a^{3} \right )y+a^{3}-b^{3}=0$ will represent the same line if<br>

Question 27 :
A straight line L through the point $(3, - 2)$ is inclined at an angle of 60$^o$ to the line $\sqrt 3 x + y = 1$. If $L$ also intersects the $x-$axis, then the equation of $L$ is

Question 28 :
The ratio between the number of passangers travelling by $1^{st}$ and $2^{nd}$ class between the two railway stations is 1 : 50, whereas the ratio of$1^{st}$ and $2^{nd}$ class fares between the same stations is 3 : 1. If on a particular day, Rs. 1325 were collected from the passangers travelling between these stations by these classes, then what was the amount collected from the $2^{nd}$ class passangers ?

Question 29 :
The equations of two equal sides of an isosceles triangle are $ 3x + 4y = 5 $and $4x - 3y = 15$. If the third side passes through $(1, 2)$, its equation is

Question 30 :
If the equations $y = mx + c$ and $x &#160;\cos &#160;\alpha + y \sin &#160;\alpha = p$ represent the same straight line, then