The students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less. If 4 students are less in a row, there would be 4 rows more. Find the number of students in the class.

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is:

The vertices of a triangle are (0,0), (6,0) and (0,8). The pair of linear equations representing two of its sides are:

A library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge.

If the point (2, 1) is the solution of the equations 2x + 3y = k and 3x - 2y = 4, find the value of k.

Which of these pairs of equations can be reduced to a pair of linear equations?

Which of the following ordered pairs (x, y) is a solution to the equation 3x - 2y = 10?

For what value of c will the system of equations x + 2y = 3 and 5x + cy = 10 be consistent and have a unique solution?

The graph of y = 3 is a line:

The graph of x = -2 is a line:

The solution of the equations x + y = 3 and 2x - y = 0 lies in which quadrant?

A and B are two points 150 km apart on a highway. A car starts from A and another from B at the same time. If they travel in the same direction, they meet in 15 hours. If they travel towards each other, they meet in 1 hour. Find the speed of the car starting from A.

For what value of k will the equations 3x + 4y = 5 and 6x + ky = 8 represent parallel lines?

The pair of equations 2x + 3y = 7 and (a-b)x + (a+b)y = 3a+b-2 has infinitely many solutions. What are the values of a and b?

If (x, y) = (2, 3) is a solution to the pair of equations 3x + ay = 15 and 2x - by = 1, then a - b is:

If x = 1, y = 2 is a solution to the equation ax + 5y = 12, then the value of 'a' is:

Which of the following pairs of linear equations represents parallel lines?

The pair of equations x = 0 and y = 0 represents:

If a pair of linear equations is consistent and dependent, then the lines are:

Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. What is the speed of the bus?

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old is Sonu now?

In the cross-multiplication method, if (a1b2 - a2b1) = 0, then the system of equations:

The line passing through the points (0, -2) and (1, 1) has the equation:

If a system of linear equations has at least one solution, it is called:

If x = a, y = b is the solution of the system of equations 2x - 3y = 1 and 4x + y = 9, find a + b.

An equation of the form y = b, where 'b' is a constant, represents a line:

An equation of the form x = a, where 'a' is a constant, represents a line:

The line 3x + 4y = 12 intersects the x-axis at:

Which of the following points lies on the line 2x - y = 5?

A part of monthly expenses of a family is fixed and the remaining varies with the number of members in the family. If there are 4 members in the family, the monthly expense is Rs 1000. If there are 7 members, the monthly expense is Rs 1300. Find the fixed expense.

The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area increases by 67 square units. Find the length and breadth of the rectangle.

The cost of 5 apples and 3 mangoes is Rs 35. The cost of 2 apples and 4 mangoes is Rs 28. What is the cost of one apple?

The sum of the digits of a two-digit number is 9. If 27 is added to the number, its digits are reversed. Find the number.

Solve: x/2 + y/3 = 13 and x/3 + y/2 = 12.

Solve: x + 2y = -1 and 2x - 3y = 12.

A pair of linear equations which has a unique solution is called a:

A pair of linear equations which has infinitely many solutions is called a:

Which of the following equations is NOT a linear equation in two variables?

How many solutions does the pair of equations x + y = 10 and x + y = 20 have?

For what value of p does the pair of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 have no solution?

For what value of k will the following pair of linear equations have infinitely many solutions? kx + 3y - (k-3) = 0 12x + ky - k = 0

If x = a and y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b are:

In the equation 2x + 3y - 5 = 0, the coefficients of x and y are respectively:

In the equation 5x - 7y = 12, the constant term is:

If a1/a2 = b1/b2 = c1/c2, what kind of lines are formed by the pair of equations?

If a1/a2 != b1/b2, what kind of lines are formed by the pair of equations?

If a1/a2 = b1/b2 != c1/c2, what kind of lines are formed by the pair of equations?

If two lines representing a pair of linear equations are coincident, then the system of equations is:

If two lines representing a pair of linear equations intersect at a single point, then the system of equations is:

If two lines representing a pair of linear equations are parallel, then the system of equations is:

A taxi charge in a city consists of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 75. For a journey of 15 km, the charge paid is Rs 110. What is the fixed charge?

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Find the speed of the stream.

A total of Rs 500 consists of notes of Rs 100 and Rs 50. If there are 7 notes in total, how many notes of Rs 100 are there?

If the numerator of a fraction is increased by 2 and the denominator by 1, the fraction becomes 1. If the numerator is decreased by 4 and the denominator by 3, the fraction becomes 1/2. Find the fraction.

The present age of a father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the father's present age.

The sum of two numbers is 10 and their difference is 4. Find the numbers.

Solve for x and y: 1/x + 1/y = 5 and 1/x - 1/y = 1.

The equations 1/x + 1/y = 5 and 1/x - 1/y = 1 can be converted to linear equations by substituting:

Solve the system: 2x + 3y = 7 and 3x - 2y = 4.

Solve the system: x + y = 5 and x - y = 1.

Solve the system: x = 2y and 3x + 4y = 20.

Which algebraic method uses a formula involving coefficients to directly find the values of x and y?

Which algebraic method involves multiplying equations by constants to make the coefficients of one variable equal, then adding or subtracting the equations?

Which algebraic method involves expressing one variable in terms of the other from one equation and substituting it into the second equation?

The graphical method of solving a pair of linear equations involves:

For what value of k do the equations 2x + 3y = 4 and (k+2)x + 6y = 3k+2 have infinitely many solutions?

For what value of k do the equations kx - 2y = 3 and 3x + y = 5 have a unique solution?

For what value of k does the pair of equations 3x + y = 1 and (2k-1)x + (k-1)y = 2 have no solution?

For what value of k does the pair of equations 3x + y = 1 and (2k-1)x + (k-1)y = 2 have a unique solution?

The pair of equations x - 2y = 0 and 3x + 4y = 20 has:

The pair of equations x + 2y = 3 and 3x + 6y = 9 has:

The pair of equations 2x + 3y = 7 and 4x + 6y = 9 has:

For a pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, to have infinitely many solutions, the condition is:

For a pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, to have no solution, the condition is:

For a pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, to have a unique solution, the condition is:

A system of linear equations is said to be inconsistent if it has:

A system of linear equations is said to be consistent if it has:

If a pair of linear equations has infinitely many solutions, what does its graph look like?

If a pair of linear equations has no solution, what does its graph look like?

If a pair of linear equations has a unique solution, what does its graph look like?

A linear equation has how many variables if its general form is ax + by + c = 0?

Which of the following is a linear equation in two variables?

A solution to a pair of linear equations in two variables (x, y) is a point that:

What is the general form of a linear equation in two variables x and y?

The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it reduces to 1/2. Find the fraction.

A two-digit number is 4 more than 6 times the sum of its digit. If 18 is subtracted from the number, the digits are reversed. Find the number.

The sum of two numbers is 137 and their difference is 43. Find the numbers.

Find the value of x and y if x + y = 5xy and 3x + 2y = 13xy . Also, x ≠ 0 and y ≠ 0

The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the numbers get reversed. The number is

The solution of the equations x + y = 14 and x – y =4 is

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?

From a bus stand in Bangalore , if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is Rs 46; but if we buy 3 tickets to Malleswaram and 5 tickets to Yeshwanthpur the total cost is Rs 74. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, find their monthly incomes.

5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

A and B each has some money. If A gives Rs. 30 to B then B will have twice the money left with A. But if B gives Rs. 10 to A then A will have thrice as much as is left with B. How much money does each have?

The difference between two numbers is 14 and the difference between their squares is 448, then find the numbers.

The sum of thrice the first and the second is 142 and four times the first exceeds the second by 138, then find the numbers.