Sample QuestionsPair of Linear Equations in Two variables questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The pair of linear equations. $\frac{3\text{x}}{2}+\frac{5\text{y}}{3}=7$ and $9\text{x}+10\text{y}=14$ is :
- A
- ✓
- C
Consistent with one solution.
- D
Consistent with many solutions.
Answer: B.
View full solution →The pair of linear equations $y = 0$ and $y = -6$ has.
- A
- ✓
- C
Infinitely many solutions
- D
Only solution $(0, 0)$
Answer: B.
View full solution →The value of $\lambda$ for which $(\text{x}_2 + 4\text{x} + \lambda)$ is a perfect square, is :
Answer: D.
View full solution →The value of $k$ for which the system of linear equations $x + 2y = 3, 5x + ky + 7 = 0$ is inconsistent is :
- A
$-\frac{14}{3}$
- B
$\frac{2}{5}$
- C
$5$
- ✓
$10$
Answer: D.
View full solution →The value of $x$ for which $2x, (x + 10)$ and $(3x + 2)$ are the three consecutive terms of an $AP,$ is :
Answer: A.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The slope of the line which lies in the second and fourth quadrant is negative.
Reason : The slope of the line $y= -x + 6$ is $-1$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $(A)$ The value of $k$ for which the system of equations $k x-y=2,6 x-2 y=3$ has a unique solution is $3$ .
Reason: $(R)$ The system of linear equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has a unique solutions, if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation for $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation for $A$.
- C
$A$ is true; $R$ is False.
- ✓
$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If a pair of linear equations is consistent, then the lines are intersecting or coincident
Reason : Because the two lines definitely have a solution.
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
Answer: A.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $3x - 4y = 7$ and $6x - 8y = k$ have infinite number of solution if $k = 14.$
Reason : $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ have a unique solution if $\frac{\text{a}_1}{\text{}a_2}\neq \frac{\text{b}_1}{\text{b}_2}$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
Answer: B.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $x$ and $y$ are $2$ different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of $x + y$ is $11$
Reason : numbers that can be formed are $xy$ and $yx$ . Hence, $(10x + y) + (10y + x) = 11(x + y)$ if this is a perfect square that $x + y = 11$
- ✓
both assertion and reason are correct and reason is correct explanation for assertion
- B
both assertion and reason are correct but reason is correct explanation for assertion
- C
assertion is correct but reason is false
- D
both assertion and reason are false
Answer: A.
View full solution →On comparing the ratios $ \frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } $ and $\frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equation is consistent, or inconsistent: 5x - 3y = 11; -10x + 6y = -22
View full solution →On comparing the ratios $\frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } } \text { and } \frac { c _ { 1 } } { c _ { 2 } }$, find out whether the pair of linear equations are consistent, or inconsistent: $\frac { 4 } { 3 } x$ + 2y = 8; 2x + 3y = 12.
View full solution →Use elimination method to find all possible solutions of the following pair of linear equations:
2x + 3y = 8 ...(1)
4x + 6y = 7 ...(2)
Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:
5x - 8y + 1 = 0; ...(i)
3x - $\frac{24}{5}$y + $\frac{3}{5}$ = 0 ...(ii)
View full solution →A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. Solve the pair of the linear equation obtained by the elimination method.
Solve the pair of linear equations by substitution method:
$\sqrt { 2 } x - \sqrt { 3 } y = 0$
$\sqrt { 3 } x - \sqrt { 8 } y = 0$
View full solution →Solve the pair of linear equations by substitution method: 3x – y = 3; 9x – 3y = 9
Is the pair of linear equation consistent/inconsistent? If consistent, obtain the solution graphically: 2x – 2y – 2 = 0; 4x – 4y – 5 = 0
Solve the following question-Aftab tells his daughter, Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. (Isn’t this interesting?) Represent this situation algebraically and graphically by the method of substitution.
Solve the following pair of equations by substitution method:
7x – 15y = 2 ...(1)
x + 2y = 3 ...(2)
Champa went to a Sale to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased. Help her friends to find how many pants and skirts Champa bought.
Check whether the pair of equations x + 3y = 6 and 2x – 3y = 12 is consistent. If so, solve them graphically.
Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received. Solve the pair of the linear equation obtained by the elimination method.
Solve the pairs of linear equation by the elimination method and the substitution method:$\frac{x}{2} + \frac{{2y}}{3} = - 1\,and\,x - \frac{y}{3} = 3$
Solve the given pair of linear equation by the elimination method and the substitution method: 3x – 5y – 4 = 0 and 9x = 2y + 7
Solve the given pair of linear equation by the elimination method and the substitution method: 3x + 4y = 10 and 2x – 2y = 2
Solve the given pair of linear equation by the elimination method and the substitution method: x + y = 5 and 2x - 3y = 4
The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball by substitution method.
Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was ₹1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was ₹3000.
Denoting the cost of 1 kg almonds by x and cost of 1 kg cashew by y, answer the following questions
- Linear equations represented by day-I and day -II situations, are
- Represent algebraically the situation of day-II.
- The linear equation represented by day-1, intersect the x axis at
Or
The linear equation represented by day-II, intersect the y-axis at
Mr Manoj Jindal arranged a lunch party for some of his friends. The expense of the lunch are partly constant and partly proportional to the number of guests. The expenses amount to 650 for 7 guests and 970 for 11 guests.
Denote the constant expense by ₹ x and proportional expense per person by ₹ y and answer the following questions.
- What is the system of linear equations representing both the situations?
- Represent both the situations algebraically.
- What is the Proportional expense for each person?
Or
The fixed (or constant) expense for the party is?
Points A and B representing Chandigarh and Kurukshetra respectively are almost 90 km apart from each other on the highway. A car starts from Chandigarh and another from Kurukshetra at the same time. If these cars go in the same direction, they meet in 9 hours and if these cars go in opposite direction they meet in 9/7 hours. Let X and Y be two cars starting from points A and B respectively and their speed be x km/hr and y km/hr respectively.
Then, answer the following questions.
- When both cars move in the same direction, then what situation can be represented as algebraically?
- When both cars move in opposite direction, then what situation can be represented as algebraically?
- what is the speed of car X?
Or
what is the speed of car Y?
From Bengaluru bus stand, if Riddhima buys 2 tickets to Malleswaram and 3 tickets to Yeswanthpur, then total cost is ₹46; but if she buys 3 tickets to Malleswaram and 5 tickets to Yeswanthpur, then total cost is ₹74.
Consider the fares from Bengaluru to Malleswaram and that to Yeswanthpur as x and y respectively and answer the following questions.
- what is the system of linear equations represented by both situations?
- 1st situation can be represented algebraically as?
- 2nd situation can be represented algebraically as?
Or
What is the Fare from Bengaluru to Malleswaram?
A part of monthly hostel charges in a college is fixed and the remaining depends on the number of days one has taken food in the mess. When a student Anu takes food for 25 days, she has to pay 4500 as hostel charges, whereas another student Bindu who takes food for 30 days, has to pay 5200 as hostel charges.
Considering the fixed charges per month by x and the cost of food per day by y, then answer the following questions.
- Represent algebraically the situation faced by both Anu and Bindu.
- Which system of linear equations is represented in above situations.
- What is the cost of food per day?
Or
What is the fixed charges per month for the hostel?