Pair of Linear Equations in Two Variables — Class 10 solved problems

37 problems from this chapter, each solved step by step.

The sum of a two-digit number and the number obtained by reversing its digits is 132. If the digits differ by 2, find the number.
The number is 75 or 57.
Two pipes, A and B, working together can fill a water tank in exactly 12 days.If pipe A works alone for half of the total time it takes for B alone to fill the
One pipe takes 21 days and the other takes 28 days (either Pipe A takes 21 days and Pipe B takes 28 days, or Pipe A takes 28 days and Pipe B takes 21 days).
7y + 2x = 10 3y+7x=9 Find x and y
x = (33)/(43), y = (52)/(43)
Determine if there exists any pair of linear equations where one line passes through (a, b) and (c, d) while the other passes through (b, a) and (d, c), such th
Yes, such a pair of linear equations exists if d + a = c + b or d + c = a + b.
Find the values of x and y for the system: 7x - 15y = 2 and x + 2y = 3
The solution to the system of equations is x = (49)/(29) and y = (19)/(29).
If 6x + 08y = 43 and x = 5 what is the value of y?
y = (13)/(8)
If 5x + 08y = 42 and x = 4 what is the value of y?
y = (11)/(4)
If 4x + 08y = 41 and x = 3 what is the value of y?
The value of y is (29)/(8).
3X+4Y = 67. If X= 3. What is Y?
Y = (29)/(2) or Y = 14.5
3X plus 5Y is equal to 40 X is equal to 2 what is the value of Y
The value of y is (34)/(5).
18 X +15 Y is equal to 3468 if X is equal to 2 or the value of Y
Y = 228.8
12 X +13 Y is equal to 140 FX is equal to 4 what is the value of Y
Y = (92)/(13)
A train covered a certain distance at a uniform speed. If the train had been 10 km/h faster, it would have taken 2 hours less than the scheduled time. If the tr
The distance covered by the train is 600 km.
5X+12Y=1280. If X=5 what is the value of Y?
Y = (1255)/(12)
Graph the line y = 2x - 3
The graph of the line y = 2x - 3 is a straight line passing through the points (0, -3) and (1, -1).
8. Solve the following system of linear equations: 3x + y = 10 x - y = 2 (system of linear equations, elimination method, substitution method)
The solution to the system of equations is x = 3 and y = 1.
Ans: 4/10 8. Solve the following system of linear equations: 3x + y = 10 x - y = 2 Ans: x=3 y=1 (system of equations, linear equations, substitution method, eli
x = 3, y = 1
Ans 4/10 8. Solve the following system of linear equations: 3x + y = 10 x - y = 2 Ans x = 3, y = 1 (system of linear equations, elimination method, substitution
x = 3, y = 1
The present age of Sahil's mother is three times the present age of Sahil. After 5 years their ages will add to 66 years. Find their present ages.
Sahil's current age is 14 years and his mother's current age is 42 years.
(a) The sum of the digits of a 2-digit number is 12. Seven times the number is equal to four times the number obtained by reversing the order of the digits. Fin
The number is 48.
If (k, 3) is the point of intersection of the lines represented by x + py = 6 and x = 15 then (k, p) will be:
(15, -3)
Draw the graph of the following equations: x + y = 5, x - y = 5, and (i) find the solution of the equations from the graph. (ii) shade the triangular region for
(i) The solution to the equations is (5, 0). (ii) The triangular region formed by the lines and the y -axis has vertices (0, 5), (0, -5), and (5, 0).
The age of the 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 p
The present age of the father is 40 years.
The condition for which the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines is:
The condition for which the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines is ab = 6.
(a) The product of the digits of a 2-digit number is 18. When 27 is subtracted from the number, the digits interchange their places. Find the number. OR (b) Two
(a) The number is 63. (b) The numbers are 40 and 48.
Solve the following pair of linear equations: x + y = 5 2x - 3y = 4
x = (19)/(5), y = (6)/(5)
what is x square - 3 x + Y = 0
The equation x² - 3x + y = 0 represents a parabola opening downwards with x-intercepts at (0, 0) and (3, 0), and its vertex at ((3)/(2), (9)/(4)).
5x + 3y = 9 (I) 2x - 3y = 12 (II) (linear equations, system of equations, variables, coefficients)
The solution to the system of equations is x=3 and y=-2.
x + y = 4 xy = 16 (system of equations, variables, algebra)
There are no real solutions for x and y.
The pair of equations x = 3 and y = - 2 graphically represent lines which are:
Perpendicular to each other
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such num
The two-digit numbers are 42 and 24. There are 2 such numbers.
Solve the following pair of equations by substitution method: 7x - 15y = 2 (1) and x + 2y = 3 (2).
The solution to the system of equations is x = (49)/(29) and y = (19)/(29).
A herd consists of camels and dromedaries. There are 180 heads and 304 bumps. How many dromedaries are there if camels have two humps each and dromedaries have
There are 56 dromedaries.
Solve the pair of linear equations: x + y = 14 and x - y = 4.
The solution to the pair of linear equations is x = 9 and y = 5.
Two rails are represented by the equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0. Will the rails cross each other?
The rails will not cross each other.
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
Aftab's present age is 42 years and his daughter's present age is 12 years.
In a shop the cost of 2 pencils and 3 erasers is ₹9 and the cost of 4 pencils and 6 erasers is ₹18. Find the cost of each pencil and each eraser. [Equations: 2x
The system of equations has infinitely many solutions. We cannot find a unique cost for each pencil and each eraser with the information provided.

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