Question 1 :
Is $3x+4y=5,\, \, 2p+7q=8$ a system of linear equations in two variables? Explain .<br/><br/><b>Answer: </b>No, because variables are not same.<br/>
Question 2 :
Age of $x$ exceeds the age of $y$ by 7yrs. This statement can be expressed as the linear equation as :<br/>
Question 3 :
The total cost of $2$ shirts and $3$ pants is $Rs.1000$ which of the following equation represent the above statement ?<br/>
Question 4 :
If $x+y=0$, which of the following must be equivalent to $x-y$?
Question 5 :
A train travelling with constant speed crosses a 96 metres long platform in 12 seconds and another 141 metres long platform in 15 seconds. The length of the train and its speed are
Question 6 : <span>Write a linear equation in two variables to represent the following statement.</span><div>The age of Jenson is less than the age of Gibin <span>by 6 years</span></div>
Question 7 : <span>Consider the equation:</span><br/><span>$\displaystyle y+7x=3x-2y+28$</span><div>If the equation is written in the form of <span>$\displaystyle ax+by=c$, then what is the value of a?<br/></span><br/></div>
Question 8 :
The taxi fare in a city is as follows : For the first kilometre, the fare is Rs.8 and for the subsequent distance it is Rs.5 per kilometre. Taking the distance covered as $x$ km and total fare as Rs.$y$, a linear equation for this information is _____.
Question 9 :
A two digit number is such that product of its digit is 18 When 63 is subtracted from the number the digit interchanged their place Find the number
Question 10 :
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Question 11 :
The number of girls in a class is $5$ times the number of boys. Which of the following cannot be the total number of children in the class?
Question 13 :
If 25% of a number is subtracted from a second number the second number reduce to its five-sixth What is the ratio of the first number to the second number?
Question 14 :
If $\displaystyle \frac{(\sqrt{a}-\sqrt{b})^{2}+4\sqrt{ab}}{a-b}=\frac{5}{3}$ then the value of a : b is
Question 15 : <div><span>State TRUE or FALSE</span><br/></div>One number is 5 more than seven times the other number.it can be represented by $x\, -\, 7y\, =\, 5$. <br/>
Question 16 :
Gopaiah sowed wheat and paddy in two fields of total area $5000$ square meters. Write a linear equation
Question 17 :
If 7x + 9y = 42 and 9x + 7y = 22, then find the value of x + y
Question 19 : <span>Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case</span><div>$2x + 3y = 9. \overline{35}$</div>
Question 20 :
If $x=a+b$ and $y=a+2b$, then what is $a-b$, in terms of $x$ and $y$ ?
Question 21 :
A machine takes 2litres of petrol to start and then 3 litres per hour while running.If the equation thus formed is of the form of ax+by+c=0 .What is the value of $a$ when linear equation is written as $\displaystyle ax+by+c=0$
Question 24 : <span>Consider the equation:</span><br/><span>$\displaystyle y+7x=3x-2y+28$</span><div>What is the value of c if the equation is written in the form <span>$\displaystyle ax+by=c$<br/></span><br/></div>
Question 25 :
<span>Write the following equations in the form $ax + by + c = 0 $, </span><span>where $a= -2,b=3$ and $c=-6$</span>
Question 26 : <span>Write the following equation as an equation in two variables:</span><div>$3y = 4$</div>
Question 29 :
If the graph of the function $y = mx + c$ passes through origin, then 'c' must be zero.
Question 30 :
A linear equation in two variable has .......... and its graph is a .......
Question 31 : <span>Write each of the following equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case.</span><div>2x + 3y = 9.35</div>
Question 32 :
What are the two possible coordinate points for the relation $x$ equals $y$ added to two?
Question 33 :
If $217\ x + 131 = 913$ and $131x + 217y = 827$, then the value of $x + y$ is _______.
Question 34 :
<span>Cost of one apple is 3 times the cost of an orange. </span>This is an example of linear equation in ..... variables.
Question 35 :
If 1.5x = 0.04y then what is the value of $\displaystyle \frac{y-x}{y+x}$ ?
Question 36 :
There are some lotus flowers in a pond and some bees are hovering around. If one bee lands on each flower, one bee will be left. If two bees land on each flower, one flower will be left. Then the number of flowers and bees respectively are __________.
Question 38 :
When simplified $\left ( x^{-1} + y^{-1} \right )^{-1}$ is equal to:
Question 39 :
Rakesh has $x$ dollars more than Mohan has, and together they have a total of $y$ dollars. Which of the following represents the number of dollars that Mohan has?<span><br></span>
Question 40 :
<span>If we write $\displaystyle 3x-7y=10$ in form of $\displaystyle ax+by+c=0,$ then $c=$</span><span>?</span>
Question 41 :
Fill in the blank:<br><span>An equation in the form ax + by + c = 0 is called ____________ equation.</span>
Question 42 :
A bag with total $10$ balls contains $x$ blue and $y$ red balls. If the number of blue balls is four times the number of red, then write the two equations.
Question 43 :
Is $5x -3y = 5$ a linear equation in one variable?
Question 45 : <span>Write a linear equation in two variables to represent the following statement.</span><div>In a one-day International cricket match between India and Sri Lanka, the two teams together scored 679 runs.</div>
Question 46 :
The solution (if exists) of a pair of linear equations represent
Question 47 :
If $(x, y) = (4, 1)$ is the solution of the pair of linear equations $mx + y = 2x + ny = 5$, then what is $m + n$ equal to?
Question 48 :
Equation $\dfrac{x}{5} - \dfrac{y}{3} = \dfrac{4}{5}$ can be expressed in the standard form as ................
Question 49 :
A train 110 metres long is running with a speed of 60 km/hr. In what time it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Question 50 :
If $\displaystyle \frac{x}{y} = \frac{4}{3}$ then $\displaystyle \frac{x^2 + y^2}{x^2 - y^2}$ is---
Question 51 :
A man buys $m$ articles at Rs. $x$ each and another $n$ articles for Rs. $y$. If he sells all the articles at Rs. $z$ per article. Frame an equation to find his profit.
