Question 1 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 2 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 4 :
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 5 :
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 6 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 7 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 8 :
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 9 :
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 10 :
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 11 :
The ratio of the present ages of mother and son is $ 12: 5$. The mother's age at the time of the birth of the son was $21$ years. Find their present ages.
Question 12 :
Find the value of x and y using cross multiplication method:<br/>$ x + 2y = 8$ and $2x -3y = 2$
Question 13 :
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 14 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{6}{x}\, -\, \frac{2}{y}\, =\, 1\,;\, \frac{9}{x}\, -\, \frac{6}{y}\,=\, 0$
Question 15 :
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 16 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:$6x = 7y +7$, $7y - x = 8$
Question 18 :
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 19 :
Solve : $\displaystyle \frac{9}{x}\, -\, \displaystyle \frac{4}{y}\, =\, 8$ and $\displaystyle \frac{13}{x}\, +\, \displaystyle \frac{7}{y}\, =\, 101$
Question 21 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: $2x - 3y= 7$, $5x + y  =9$
Question 22 :
If $2x=t+\sqrt{t^2+4}$ and $3y=t-\sqrt{t^2+4}$ then the value of  $y$ when $x=\dfrac {2}{3}$, is ____.
Question 23 :
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 24 :
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 25 :
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 26 :
Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is
Question 27 :
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 28 :
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.
