Question 2 :
If x and y are positive with $x-y=2$ and $xy=24$ , then $ \displaystyle \frac{1}{x}+\frac{1}{y}$   is equal to
Question 3 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 4 :
In a zoo there are some pigeons and some rabbits. If their heads are counted these are $300$ and if their legs are counted these are $750$ How many pigeons are there?
Question 6 :
Equation of a straight line passing through the origin and making an acute angle with $x-$axis twice the size of the angle made by the line $y=(0.2)\ x$ with the $x-$axis, is:
Question 7 :
Some students are divided into two groups A & B. If $10$ students are sent from A to B, the number in each is the same. But if $20$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.<br/>
Question 8 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 9 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 10 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 
Question 12 :
Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.
Question 14 :
State whether the given statement is true or false:The graph of a linear equation in two variables need not be a line.<br/>
Question 15 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 16 :
Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is
Question 17 :
A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?
Question 18 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 19 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.
Question 21 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 22 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at
Question 23 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is
Question 26 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 28 :
The  linear equation, such that each point on its graph has an ordinate $3$ times its abscissa is $y=mx$. Then the value of $m$ is<br/>
Question 29 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<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 30 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 31 :
The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two. 
Question 32 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 33 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 34 :
Assem went to a stationary shop and purchased $3$ pens and $5$ pencils for $Rs.40$. His cousin Manik bought $4$ pencils and $5$ pens for $Rs. 58$. If cost of $1$ pen is $Rs.x$, then which of the following represents the situation algebraically?
Question 35 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 36 :
Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the coordinates of the intersection of other line with the cordinate axes.
Question 37 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 39 :
If the system of equation, ${a}^{2}x-ay=1-a$ & $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:
Question 40 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 41 :
State whether the given statement is true or false:Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.<br/>
Question 42 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is
Question 43 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 44 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 45 :
The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point
Question 46 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 48 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 49 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 50 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 51 :
Solve: $\displaystyle \frac{3}{x}\, -\, \displaystyle \frac{2}{y}\, =\, 0$ and $\displaystyle \frac{2}{x}\, +\, \displaystyle \frac{5}{y}\, =\, 19$<br/>Hence, find 'a' if $y\, =\, ax\, +\, 3$
Question 52 :
Solve the following pair of equations by the elimination method and the substitution method:<br/>$3x - 5y - 4 = 0$ and $9x = 2y + 7$<br/>
Question 53 :
Solve the following pair of equations by cross multiplication rule.<br/>$ax + by + a = 0, bx + ay + b = 0$
Question 55 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence, find $a$ if $y= ax-2$
Question 56 :
a, b, c (a > c) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit's place. The other two digits from left to right are -
Question 57 :
Solve the equations using elimination method:<br>$x - 6y = 9$ and $2x - y = 7$
Question 59 :
Solve the following pair of simultaneous equations:$\displaystyle\,3x\, +\, \frac{1}{y}\, =\, 13\, ;\, \frac{2}{y}\, -\, x\, =\, 5$
Question 60 :
Solve the following simultaneous equations :$\displaystyle \frac{1}{3x}\, +\, \frac{1}{5y}\, =\, \frac{1}{15};\quad \frac{1}{2x}\, +\, \frac{1}{3y}\, =\, \frac{1}{12}$
Question 61 :
Solve : $\displaystyle \frac{3}{x+y}+\displaystyle \frac{2}{x-y}= 2$ and $\displaystyle \frac{9}{x+y}-\displaystyle \frac{4}{x-y}= 1$
Question 64 :
Number of ordered pair(s) of (x, y) satisfying the system of simultaneous equations$\displaystyle \left | x^{2}-2x \right |+y=1\: \: and\: \: x^{2}+\left | y \right |=1\: \: is\: \: \left ( x,y\: \epsilon \: R \right )$
Question 66 :
In the system of equations $4(x + 3) -3(y + 1) =4$ and $3(x -1) + (2y -3) =20$, the values of $x$ and $y$ are:
Question 67 :
In the system of equations $\dfrac {12}{x+y}+\dfrac {8}{x-y}=8$ and $\dfrac {27}{x+y}-\dfrac {12}{x-y}=3$, the values of $x$ and $y$ will be
Question 68 :
Solve the following simultaneous equations :$\displaystyle \frac{16}{x + y}\, +\, \frac{2}{x - y}\, =\, 1;\quad \frac{8}{x + y}\, -\, \frac{12}{x - y}\, =\, 7$
Question 69 :
Find the value of x and y using cross multiplication method: <br>$x - 6y = 2$ and $x + y = 4$
Question 70 :
Solve the following pair of equations:<br/>$\displaystyle \frac{9}{x}-\displaystyle \frac{4}{y}= 8$, $\displaystyle \frac{13}{x}+\displaystyle \frac{7}{y}=101$
Question 71 :
The sum of a two digit number and the number obtained by reversing the order of its digits is $121$, and the two digits differ by $3$. Find the number.
Question 73 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, =\, 5\,;\, \frac{1}{x}\, -\, \frac{1}{y}\, =\, 1$
Question 74 :
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Question 75 :
Solve the following pair of equations by cross multiplication rule.$x + y = a + b, ax - by = a^2-b^2$<br/>
Question 76 :
The difference between a two digit number and the number obtained by the interchanging the digits is $27$. What is the difference between the two digits of the number?
Question 77 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {10}{(x+y)}+\dfrac {2}{(x-y)}=4, \dfrac {15}{(x+y)}-\dfrac {5}{(x-y)}=-2$<br/>
Question 79 :
Solve each of the following system of equations by elimination method. $13x +11y=70, 11x+13y=74$
Question 80 :
Solve the following simultaneous equations by the method of equating coefficients.$x-2y=-10; \, \, 3x-5y=-12$
Question 81 :
Solve the following pairs of linear equations by elimination method:<br/>$217x + 131y = 913$ and $131x + 217y = 827$<br/>
Question 83 :
Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$
Question 84 :
Solve each of the following system of equations by elimination method. $65x-33y=97, 33x-65y=1$
Question 85 :
With Rs. $1000$ a rancher is to buy steers at Rs. $25$ each and cows at Rs. $26$ each. If the number of steers $s$ and the number of cows $c$ are both positive integers, then:
Question 86 :
Let the equation $x + y +z = 5, x + 2y + 2z = 6, x + 3y + \lambda z = \mu$ have infinite solution then the value of $\lambda \mu $ is$10$
Question 87 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\,  \displaystyle \frac{8}{y}\, =\, 14$<br/>Hence, find 'a' if $y\, =\, ax\, -\, 2$
Question 88 :
Find the value of x and y using cross multiplication method: <br>$5x + 2y = 32$ and $6x + 6y = 42$
Question 89 :
If $6$ kg of sugar and $5$ kg of tea together cost Rs. $209$ and $4$ kg of sugar and $3$ kg of tea together cost Rs. $131$, then the cost of $1$ kg sugar and $1$ kg tea are respectively<br/>
Question 90 :
Solve the equations using elimination method:<br>$x + 3y = 8$ and $x + 2y = 8$<br>
Question 91 :
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. The present ages, in years, of the son and the father are respectively,
Question 92 :
If $bx+ay=a^2+b^2$ and $ax-by=0$, then the value of $(x-y) $ is<br/>
Question 93 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$
Question 94 :
Solve the following pair of equations :$x\, -\, y\, =\, 0.9$<br/>$\displaystyle \frac{11}{2\, (x\, +\, y)}\, =\, 1$
Question 95 :
Based on equations reducible to linear equations<br/>Solve for x and y: $\dfrac {11}{2x}-\dfrac {9}{2y}=-\dfrac {23}{2}; \dfrac {3}{4x}+\dfrac {7}{15y}=\dfrac {23}{6}$<br/>
Question 96 :
Find the value of x and y using cross multiplication method: <br/>$x-  2y = 1$ and $x + 4y = 6$
Question 97 :
What is the value of $a$ for the following equation: $3a + 4b = 13$ and $a + 3b = 1$? (Use cross multiplication method).<br/>
Question 98 :
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 99 :
If the product of two numbers is $10$ and their sum is $7$, which is the greatest of the two numbers?
Question 100 :
The expression ax + b is equal to 13 when x is 5and ax + b is equal to 29 when x is 13. The valueof expression when x is 0.5
Question 101 :
Father's age is three times the sum of ages of his two children. After $5$ years his age will be twice the sum of ages of two children. Find the age of father.<br/>
Question 102 :
The cost of an article $A$ is $15$% less than that of article $B.$ If their total cost is $2,775\:Rs\:;$ find the cost of each article$.$ <br>
Question 103 :
The equation of the straight line which passes through $(1, 1)$ and making angle $60^o$ with the line $x+ \sqrt 3y +2 \sqrt 3=0$ is/are.
Question 104 :
The axes being inclined at an angle of $30^o$, the equation of straight line which makes an angle of $60^o$ with the positive direction of x-axis and x-intercept 2 is
Question 105 :
Based on equations reducible to linear equations<br/>Solve for x and y: $\dfrac {24}{2x+y}-\dfrac {13}{3x+2y}=2; \dfrac {26}{3x+2y}+\dfrac {8}{2x+y}=3$
Question 106 :
Based on equations reducible to linear equations, solve for $x$ and $y$:<br/>$\dfrac {x-y}{xy}=9; \dfrac {x+y}{xy}=5$<br/>
Question 107 :
A line perpendicular to the line $\displaystyle 3x-2y=5$ cuts off an intercept $3$ on the positive side of the $x$-axis. Then 
Question 108 :
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 109 :
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 110 :
If the equations $y = mx + c$ and $x  \cos  \alpha + y \sin  \alpha = p$ represent the same straight line, then
Question 111 :
Equations of the two straight lines passing through the point $(3, 2)$ and making an angle of $45 ^ { \circ }$ with the line $x - 2 y = 3$, are
Question 112 :
Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is
Question 113 :
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 114 :
A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^{o}$ to the line $\sqrt{3}x+y=1$. lf $L$ also intersects the $x-$axis, then the equation of $L$ is<br>
Question 115 :
Based on equations reducible to linear equations<br/>Solve for x and y: $\dfrac {16}{x+3}+\dfrac {3}{y-2}=5; \dfrac {8}{x+3}-\dfrac {1}{y-2}=0$<br/>
Question 116 :
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 117 :
The equation of the line passing through the point $P(1, 2)$ and cutting the lines $x + y - 5 = 0$ and $2x - y = 7$ at $A$ and $B$ respectively such that the harmonic mean of $PA$ and $PB$ is $10$, is
Question 118 :
The sum of three numbers is $92$. The second number is three times the first and the third exceeds the second by $8$. The three numbers are: 
Question 119 :
A line has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through an angle $\alpha $, keeping the origin fixed, the line makes equal intercepts on the coordinate axes, then $\tan$ <br> $\alpha $=<br/>
Question 120 :
Equation of a straight line passing through the point $(2, 3)$ and inclined at an angle of $\tan^{-1} \left(\dfrac{1}{2}\right)$ with the line $y + 2x = 5$ is
