Question 2 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 5 :
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 6 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 7 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 8 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 9 :
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 10 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 11 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<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 12 :
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 15 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 16 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 17 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 18 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 19 :
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 21 :
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 22 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 23 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 24 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is
Question 26 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$2x+7y= 39$<br/>$3x+5y= 31$
Question 27 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, =\, 5\,;\, \frac{1}{x}\, -\, \frac{1}{y}\, =\, 1$
Question 28 :
Solve the following pair of equations by cross multiplication rule.<br/>$ax + by + a = 0, bx + ay + b = 0$
Question 29 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$0.2x+0.1y= 25$<br/>$2\left ( x-2 \right )-1.6y= 116$
Question 30 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence find the value of $k$, if $y= kx-2$.
Question 31 :
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 32 :
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 33 :
Solution of the equations $\cfrac{x + 3}{4} + \cfrac{2y + 9}{3} = 3$ and $\cfrac{2x - 1}{2} - \cfrac{y + 3}{4} = 4 \cfrac{1}{2}$ is<br/>
Question 34 :
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Question 36 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{8}{x}\, -\, \frac{9}{y}\, =\, 1;\,\frac{10}{x}\, +\, \frac{6}{y}\, =\, 7$
Question 38 :
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 40 :
Solve the following simultaneous equations by the method of equating coefficients.$x-2y=-10; \, \, 3x-5y=-12$
Question 41 :
Solve the set of equations: $3\left ( 2u+v \right )= 7uv$ and $3\left ( u+3v \right )= 11uv$
Question 42 :
Solve the equations using elimination method:<br>$x - 4y = -20$ and $4x + 4y = 20$
Question 43 :
Based on equations reducible to linear equations, Solve for x and y:$6x + 5y = 8xy$ and $ 8x + 3y = 7xy$<br>
Question 44 :
If $1$ is added to each of the two certainnumbers, their ratio is $1:2$; and if $5$issubtracted from each of the two numbers, theirratio becomes $5:11$. Find the numbers.
Question 45 :
Solve the equations using elimination method:<br>$2x + y = 2$ and $x - y = 4$
Question 46 :
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 47 :
Solve the following pair of simultaneous equations:$\displaystyle\, y\, -\, \frac{3}{x}\, =\, 8\, ;\, 2y\, +\, \frac{7}{x}\, =\, 3$
Question 48 :
What is the value of $x$ for the following equations: $x - 5y = 10$ and $x + y =4$? (Use cross multiplication method).<br/>
Question 49 :
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 50 :
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 51 :
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 52 :
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 53 :
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 54 :
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 55 :
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 56 :
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 57 :
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 58 :
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 59 :
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 60 :
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
