Question 1 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is
Question 2 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 3 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 4 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 5 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.
Question 6 :
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 7 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 8 :
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 10 :
The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point
Question 11 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 12 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 14 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 15 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 16 :
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 17 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 20 :
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 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 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 24 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 25 :
Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:
Question 26 :
Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.
Question 27 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 29 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 30 :
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 31 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 32 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<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 33 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 36 :
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 37 :
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 38 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 39 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is
Question 40 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 
Question 42 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 43 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 44 :
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 45 :
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 46 :
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 47 :
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 49 :
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 50 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at
Question 52 :
Solve the following pairs of equations by reducing them to a pair of linear equations.<br/>$\displaystyle \frac{3}{x+1}-\frac{1}{y+1}=2$ and $\dfrac{6}{x+1}-\dfrac{1}{y+1}=5$
Question 53 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: $2x - 3y= 7$, $5x + y  =9$
Question 54 :
Solve each of the following system of equations by elimination method. $13x +11y=70, 11x+13y=74$
Question 55 :
Solve the following pair of equations:<br/>$\displaystyle \frac{6}{x}+\displaystyle \frac{4}{y}= 20, \displaystyle \frac{9}{x}-\displaystyle \frac{7}{y}= 10.5$
Question 56 :
Solve the equations using elimination method:<br>$2x + 3y =15$ and $3x + 3y = 12$
Question 57 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\displaystyle \frac {2}{\sqrt x}+\frac {3}{\sqrt y}=2, \frac {4}{\sqrt x}-\frac {9}{\sqrt y}=-1$<br/>
Question 58 :
Solve the following pair of equations by cross multiplication rule.$x + y = a + b, ax - by = a^2-b^2$<br/>
Question 59 :
Solve the equations using cross multiplication method: $3x + 2y = 10$ and $4x - 2y = 4$<br/>
Question 60 :
Solve the following pair of equations:<br/>$\displaystyle \frac{a}{x}\, -\, \displaystyle \frac{b}{y}\, =\, 0$<br/>$\displaystyle \frac{ab^{2}}{x}\, +\, \displaystyle \frac{a^{2}b}{y}\, =\, a^{2} \, +\, b^{2}$
Question 61 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\, \displaystyle \frac{8}{y}\, =\, 14$
Question 62 :
Solve the following pairs of linear equations by elimination method:<br/>$217x + 131y = 913$ and $131x + 217y = 827$<br/>
Question 63 :
Solve the following pair of simultaneous equations:$\displaystyle\, y\, -\, \frac{3}{x}\, =\, 8\, ;\, 2y\, +\, \frac{7}{x}\, =\, 3$
Question 64 :
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 65 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\,  \displaystyle \frac{8}{y}\, =\, 14$<br/>Hence, find 'a' if $y\, =\, ax\, -\, 2$
Question 66 :
Determine the values of a and b for which the following system of linear equation has infinite solutions.<br>$2x-(a-4)y=2b+1$<br>$4x-(a-1)y=5b-1$<br>
Question 67 :
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 68 :
Solve the following pair of equations by reducing them to a pair of linear equations:$\dfrac {4}{x}+3y=14, \dfrac {3}{x}-4y=23$<br/>
Question 69 :
Find the value of x and y using cross multiplication method: <br>$x - 6y = 2$ and $x + y = 4$
Question 70 :
For what value of $\alpha$, the system of equations<br>$\alpha x+3y=\alpha-3$<br>$12x+\alpha y=\alpha$<br>will have no solution
Question 71 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{a}{4}\, -\, \frac{b}{3}\, =\, 0\,;\, \frac{3a\, +\, 8}{5}\, =\, \frac{2b\, -\, 1}{2}$
Question 72 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:$y =\, 4x\, -\, 7$, $16x\, -\, 5y\, =\, 25$
Question 73 :
Solve each of the following system of equations by elimination method. $65x-33y=97, 33x-65y=1$
Question 74 :
If $\displaystyle \frac{x+y-8}{2} = \frac{x+2y-14}{3}=\frac{3x-y}{4}$, then the values of $x$ and $y$ is
Question 75 :
Solve: $\displaystyle \frac{20}{x\, +\, y}\, +\, \displaystyle \frac{3}{x\, -\,y}\, =\, 7$ and $\displaystyle \frac{8}{x\, -\, y}\, -\, \displaystyle \frac{15}{x\, +\, y}\, =\, 5$
Question 76 :
Solve the following simultaneous equations by the method of equating coefficients.$x-2y=-10; \, \, 3x-5y=-12$
Question 77 :
Solve the following simultaneous equations :$\displaystyle \frac{27}{x-2}\, +\, \frac{31}{y + 3}\, =\, 85;\quad \frac{31}{x - 2}\, +\, \frac{27}{y + 3}\, =\, 89$
Question 78 :
Solve the following pair of simultaneous equations:$8a\, -\, 7b\, =\, 1$<br/>$4a\, =\, 3b\, +\, 5$
Question 80 :
One pendulum ticks $57$ times in $58$ seconds and another $608$ times in $609$ seconds. If they start simultaneously, find the time after which will they tick together?
Question 81 :
Solve the equations using elimination method:<br>$3x + 2y = 7$ and $4x - 3y = -2$
Question 82 :
Based on equations reducible to linear equations, Solve for x and y:$6x + 5y = 8xy$ and $ 8x + 3y = 7xy$<br>
Question 83 :
If $\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}} = \dfrac{10}{3}$ and $ x + y = 10$, find the value of $xy.$
Question 84 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {1}{(3x+y)}+\dfrac {1}{(3x-y)}=\dfrac {3}{4},\  \dfrac {1}{2(3x+y)}-\dfrac {1}{2(3x-y)}=\dfrac {-1}{8}$
Question 85 :
Find the value of x and y using cross multiplication method:<br/>$ x + 2y = 8$ and $2x -3y = 2$
Question 86 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{8}{x}\, -\, \frac{9}{y}\, =\, 1;\,\frac{10}{x}\, +\, \frac{6}{y}\, =\, 7$
Question 87 :
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:The sum of the digits of a two-dlgit number is $9$. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number<br/>
Question 88 :
Solve the following simultaneous equations by the method of equating coefficients.$\displaystyle \frac{x}{3}+\frac{y}{4}=4; \, \, \frac{5x}{6}-\frac{y}{8}=4$
Question 89 :
Solve the equations using elimination method:<br>$x - 4y = -20$ and $4x + 4y = 20$
Question 90 :
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 91 :
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Question 93 :
Solve the following pair of equations:<br/>$\displaystyle \frac{1}{5}\left ( x-2 \right )=\displaystyle \frac{1}{4}\left ( 1-y \right )$, $26x+3y+4= 0$
Question 94 :
Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$
Question 95 :
Find the value of x and y using elimination method:<br/>$\dfrac{-1}{x} + \dfrac{2}{y} = 0$ and $\dfrac{x}{2}+  \dfrac{y}{3} = 1$<br/>
Question 96 :
If the product of two numbers is $10$ and their sum is $7$, which is the greatest of the two numbers?
Question 97 :
Find the solution of $x$ and $y$ using cross multiplication method: $3x - y = 1$ and $x + 2y = 5$<br/>
Question 98 :
Find the values of $x$ and $y$, if $\displaystyle \frac{2}{x}\, +\, \frac{6}{y}\, =\, 13;\quad \frac{3}{x}\, +\, \frac{4}{y}\, =\, 12$
Question 100 :
Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. If present ages of Aarushi and Ravish are <b>x</b> and <b>y </b>years respectively, represent this situation algebraically and find their present ages.
Question 101 :
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 102 :
Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is
Question 103 :
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 104 :
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 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<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 107 :
If the equations $y = mx + c$ and $x  \cos  \alpha + y \sin  \alpha = p$ represent the same straight line, then
Question 108 :
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 109 :
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 110 :
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 111 :
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 112 :
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 113 :
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
Question 114 :
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 115 :
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 117 :
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 118 :
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 119 :
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 120 :
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 121 :
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
