Pair of Linear ...

The cost of 3 pencils boxes and 3 erasers boxes is Rs. 150. Four times the cost of pencil box is 20 more than the cost of eraser box. Find the respective costs of a pencil box and an eraser box.

The sum of the digits of a two-digit number is 9. Also, half of this number is 9 more than the number obtained by reversing the order of digits. Find the number.

Which of the following sets of equations does not have a unique solution?

Which of the following values of p is not correct for the system of equations pm – 4n = 8 and 24m – 8n = 12 to have a unique solution?

The pair of equations 15p – 45q = 24 and 6p – 18q =has

Find the respective values of m and n from the following pair of linear equations:

m – n = 9

+ = 14

The ratio of incomes of Rama and Ravi is : and the ratio of their expenditures is to , respectively. If each of them saves Rs. 300 per month, find their expenditures.

Solve for x:

+= 1 and+=

Which of the following linear equations is parallel to the line 18x + 36y - 108 = 0?

The sum of the numerator and the denominator of a fraction is 7. If we add 2 to the numerator and subtract 1 from the denominator, then the fraction becomes . What is the value of three times the original fraction?

The numerator of a rational number is greater than its denominator by 12. If 9 subtracted from the numerator and 5 is added to the denominator, the new rational number becomes. Find the original rational number.

Which of the following can be the values of x and y if and?

Find the value of 11x - 7y, if 17x + 19y = 650 and 23x - 13y = 144.

If the following lines are coincident, then what will be the value of k?

5x + 7y + 15 = 12
15x + 21y + k = 10

Harmeet and Manmeet were playing with marbles. When they started playing, Harmeet lost 10 of his marbles to Manmeet and the ratio of marbles of Harmeet to those of Manmeet became 5 : 4. After some time, Manmeet lost 20 of his marbles to Harmeet and the ratio of marbles of Harmeet to those of Manmeet became 7 : 2. Find the difference between the marbles they had at the beginning.

In a box, there are 10 pens in total, out of which some are blue and some are red. When twice the number of blue pens is added to three times the number of red pens, the result obtained is 23. How many red pens are there in the box?

A boat can cover 30 km going upstream in 20 minutes and 40 km going downstream in 24 minutes. How much time will the boat take to travel 84 km downstream if the speed of the stream is doubled?

The difference between the age of Guri and Shuri is 4 years. Five years ago, the sum of their ages was 36 years. What will be the ratio of the age of Guri to that of Shuri 7 years from now, if Shuri is younger than Guri?

The cost of 3 mangoes and 4 oranges is Rs. 29, and that of 4 mangoes and 3 oranges is Rs. 27. If 5 mangoes and 5 oranges are sold at a profit of 25% in total, what will be the total selling price of 5 mangoes and 5 oranges?

Which of the following values of x and y represent the solution of the pair of equations 2a₁x + b₁y – c₁ = 0 and 2a₂x + b₂y – c₂ = 0?

Fill in the blanks:

(i) When the lines representing the equations are intersecting at a single point, then it has _____ solutions.
(ii) If of the pair of linear equations and , then the pair of linear equations has _____ solutions.
(iii) If the pair of linear equations is inconsistent, then the lines are _____.

Which of the following statements is false?

A. y + 3x = 0 and 12y + 23x = 0, both the lines pass through the origin.
B. The pair of equations 8x + 6y = 15 and 3x – 4y = 25 has a unique solution.
C. 2x + 6y = 12 and 8x + 24y = 48 are an inconsistent pair of equations.
D. x + 6y = 12 and x + 6y = 16 are an inconsistent pair of equations.

Which of the following pairs of linear equations has/have solution (x, y) that are positive rational number?

(i) 3x + 2y = 10 and 4x + 3y – 9 = 0
(ii) 5x + 2y + 4 = 0 and 2x + 3y + 6 = 0
(iii) 2x +y = 9 and x + 5y – = 0
(iv) and

Match the following.

System of equations	Solutions
(a) 2x + y = 7 and y = 8 + x	(i) x = -2, y = 1
(b) x + 7y = 9 and 3x + y = 21	(ii) No solution
(c) x + 4 = 2y and x + 3 = y	(iii) x = , y =
(d) x + 8 = y and 2y = 12 + 2x	(iv) x = , y =

Which of the following graphs represent the parallel lines of equations, 2x - 5 + 3y = 0 and 4x - 12 = -6y?