Question 1 : The graph of the linear equation $2x -y = 4$ cuts x-axis at

Question 3 : 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 4 : If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is

Question 5 : $\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<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 6 : 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 7 : The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is

Question 8 : 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 9 : 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 11 : What is the nature of the graphs of a system of linear equations with exactly one solution?

Question 12 : 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.&#160;

Question 14 : Some&#160;students&#160;are&#160;divided&#160;into&#160;two&#160;groups&#160;A&#160;&amp;&#160;B.&#160;If $10$ students are sent from A to B, the&#160;number in each is the same.&#160;But if $20$ students are sent from B to A, the number in A is double&#160;the number in B. Find the number of students in each group A &amp; B.<br/>

Question 15 : The linear equation $y = 2x + 3$ cuts the $y$-axis at&#160;

Question 16 : Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$

Question 18 : Examine whether the&#160;point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.

Question 19 : The sum of two numbers is $2$ and their difference is $1$. Find the numbers.

Question 20 : The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be&#160;

Question 21 : 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 22 : 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 26 : If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then&#160;find $a$.

Question 27 : The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point

Question 28 : If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ 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 : If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies

Question 32 : Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is

Question 33 : 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 34 : Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$

Question 36 : If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is

Question 37 : A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is

Question 39 : If $2x + y = 5$, then $4x + 2y$ is equal to _________.

Question 41 : If the system of equation, ${a}^{2}x-ay=1-a$ &amp; $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:

Question 42 : 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 43 : What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.

Question 44 : The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point

Question 45 : 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 46 : If x and y are positive with $x-y=2$ and $xy=24$ , then&#160;$ \displaystyle \frac{1}{x}+\frac{1}{y}$ &#160; is equal to

Question 47 : A line which passes through (5, 6) and (-3. -4) has an equation of

Question 48 : The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is

Question 49 : 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 50 : 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 51 : 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 52 : What is the value of $a$ for the following equation: $3a + 4b = 13$ and $a + 3b = 1$?&#160;(Use cross multiplication method).<br/>

Question 53 : Based on equations reducible to linear equations<br/>Solve for x and y&#160;$\dfrac {2}{x}+\dfrac {3}{y}=2; \dfrac {1}{x}-\dfrac {1}{2y}=\dfrac {1}{3}$

Question 55 : The simultaneous equations,&#160;$\displaystyle y = x + 2|x| $ &amp; $y = 4 + x - |x|$ have the solution set&#160;

Question 56 : Solve the equations using elimination method:<br>$x - 4y = -20$ and $4x + 4y = 20$

Question 57 : If $\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}} = \dfrac{10}{3}$ and $ x + y = 10$, find the value of $xy.$

Question 58 : Solve the equations using elimination method:<br>$2x + 3y = 12$ and $4x + 2y = 8$

Question 59 : 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 60 : 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 62 : Based on equations reducible to linear equations, Solve for x and y:$6x + 5y = 8xy$ and $ 8x + 3y = 7xy$<br>

Question 63 : 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 65 : Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:$y =\, 4x\, -\, 7$,&#160;$16x\, -\, 5y\, =\, 25$

Question 66 : Solve the following pair of simultaneous equations:$\displaystyle\,3x\, +\, \frac{1}{y}\, =\, 13\, ;\, \frac{2}{y}\, -\, x\, =\, 5$

Question 67 : Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$

Question 68 : If$\displaystyle \frac{x+y}{x-y}=\frac{5}{3}\: and\: \frac{x}{\left ( y+2 \right )}=2$ the value of (x , y) is

Question 69 : Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$

Question 70 : Solve the equations using elimination method:<br>$x - 6y = 9$ and $2x - y = 7$

Question 72 : 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 73 : Solve the equations using elimination method:<br>$2x + 3y =15$ and $3x + 3y = 12$

Question 74 : 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 75 : 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 76 : If the product of two numbers is $10$ and their sum is $7$, which is the greatest of the two numbers?

Question 77 : Solve the following pairs of equations by reducing them to a pair of linear equations:<br>$\displaystyle \dfrac {7x-2y}{xy}=5, \dfrac {8x+7y}{xy}=15$<br>

Question 78 : Solve the following pair of simultaneous equations:$\displaystyle \frac{3}{a}\, +\, \frac{4}{b}\, =\, 2\,;\, \frac{9}{a}\, -\, \frac{4}{b}\, =\, 2$

Question 79 : 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 83 : If $2p + 3q = 18$ and $4p^{2} + 4pq - 3q^{2} - 36 = 0$ then what is $(2p + q)$ equal to?

Question 84 : Solve the equations using cross multiplication method: $3x + 2y = 10$ and $4x - 2y = 4$<br/>

Question 85 : 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 86 : 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 87 : Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$.&#160;Hence find the value of $k$, if $y= kx-2$.

Question 88 : Solve the following pairs of linear equations by elimination method:<br/>$217x + 131y = 913$ and $131x + 217y = 827$<br/>

Question 89 : 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 90 : Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$2x+7y= 39$<br/>$3x+5y= 31$

Question 91 : If $y=a+\cfrac { b }{ x } $, where $a$ and $b$ are constants, and if $y=1$ when $x=-1$, and $y=5$ when $x=-5$, then $a+b$ equals.

Question 92 : Find the value of x and y using cross multiplication method: <br>$3x + 4y = 43$ and $-2x + 3y = 11$

Question 93 : Solve the following simultaneous equations by the method of equating coefficients.$\displaystyle \frac{x}{2}+3y=11; \, \, x+5y=20$

Question 94 : 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 95 : 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 96 : Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac{2x-3y}{xy}=4$ and $\dfrac{15x+3y}{xy}=30$

Question 97 : Solve the following pair of simultaneous equations:$\displaystyle \frac{6}{x}\, -\, \frac{2}{y}\, =\, 1\,;\, \frac{9}{x}\, -\, \frac{6}{y}\,=\, 0$

Question 98 : Solve: $\displaystyle \frac{3}{x}-\displaystyle \frac{2}{y}= 0$ and $\displaystyle \frac{2}{x}+\displaystyle \frac{5}{y}= 19$. Hence, find $a$ if $y= ax+3$.

Question 99 : If $2x + y = 23$ and $4x - y = 19$; find the values of $x - 3y$ and $5y - 2x$.<br/>

Question 100 : The number of solutions for the system of equations $2x + y = 4, 3x + 2y = 2$ and $x + y = - 2$ is

Question 101 : 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 102 : 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 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 line perpendicular to the line $\displaystyle&#160;3x-2y=5$ cuts off an intercept $3$ on the positive side of the $x$-axis. Then&#160;

Question 105 : 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 106 : 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 107 : 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 108 : Based on equations reducible to linear equations<br/>Solve for x and y:&#160;$\dfrac {16}{x+3}+\dfrac {3}{y-2}=5; \dfrac {8}{x+3}-\dfrac {1}{y-2}=0$<br/>

Question 109 : 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 110 : 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 111 : Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is

Question 112 : Based on equations reducible to linear equations<br/>Solve for x and y:&#160;$\dfrac {24}{2x+y}-\dfrac {13}{3x+2y}=2; \dfrac {26}{3x+2y}+\dfrac {8}{2x+y}=3$

Question 113 : 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 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:&#160;

Question 115 : If the equations $y = mx + c$ and $x &#160;\cos &#160;\alpha + y \sin &#160;\alpha = p$ represent the same straight line, then

Question 116 : 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 118 : The equation of the straight line which passes through $(1, 1)$ and making angle $60^o$ with the line&#160;$x+ \sqrt 3y +2 \sqrt 3=0$ is/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 : 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 121 : 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