Question 1 :
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 2 :
The unit digit of a number is $$x$$ and its tenth digit is $$y$$ then the number will be 
Question 3 :
If $$x + y = 25$$ and $$\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$$, then the value of $$x - y$$ is
Question 4 :
The sum of two numbers is $$2$$ and their difference is $$1$$. Find the numbers.
Question 5 :
If $$(a, 3)$$ is the point lying on the graph of the equation $$5x\, +\, 2y\, =\, -4$$, then find $$a$$.
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 8 :
The graph of the line $$5x + 3y = 4$$ cuts the $$y$$-axis at the point
Question 10 :
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 11 :
The solution of the simultaneous equations $$\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $$ is given by
Question 12 :
A member of these family with positive gradient making an angle of$$\frac{\pi }{4}$$ with the line3x-4y=2, is
Question 13 :
If the equations $$4x + 7y = 10 $$ and $$10x + ky = 25$$ represent coincident lines, then the value of $$k$$ is
Question 14 :
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 15 :
Solve the following equations:<br/>$$x + \dfrac {4}{y} = 1$$,<br/>$$y + \dfrac {4}{x} = 25$$.Then $$(x,y)=$$
Question 16 :
Choose the correct answer which satisfies the linear equation: $$2a + 5b = 13$$ and $$a + 6b = 10$$
Question 18 :
If $$p+q=1$$ andthe ordered pair (p, q) satisfies $$3x+2y=1$$,then it also satisfies
Question 19 :
The graph of the lines $$x + y = 7$$ and $$x - y = 3$$ meet at the point
Question 20 :
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 21 :
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 22 :
$$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$$<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 23 :
The number of pairs of reals (x, y) such that $$x =x^2+y^2$$ and $$y =2xy$$ is
Question 24 :
Examine whether the point $$(2, 5)$$ lies on the graph of the equation $$3x\, -\, y\, =\, 1$$.
Question 25 :
The graph of the linear equation $$2x -y = 4$$ cuts x-axis at
Question 26 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 29 :
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 30 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 31 :
Solve the following pair of equations by reducing them to a pair of linear equations:$$6x + 3y = 6xy, 2x + 4y = 5xy$$<br/>
Question 32 :
Find the value of x and y using cross multiplication method: <br>$$3x - 5y = -1$$ and $$x + 2y = -4$$
Question 33 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:$$6x = 7y +7$$, $$7y - x = 8$$
Question 34 :
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 35 :
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 36 :
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 37 :
Solve the equations using elimination method:<br>$$2x + 3y =15$$ and $$3x + 3y = 12$$
Question 38 :
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 39 :
Solve: $$4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$$ and $$6x\, -\,  \displaystyle \frac{8}{y}\, =\, 14$$<br/>Hence, find 'a' if $$y\, =\, ax\, -\, 2$$
Question 40 :
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.
