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Pair of Linear Equations

The document contains a series of mathematical problems related to linear equations in two variables, including solving pairs of equations, determining fixed and variable costs, graphing equations, and analyzing the relationship between lines. It also includes word problems involving two-digit numbers and the dimensions of a rectangle. Each problem varies in complexity and requires different methods for solution.

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suzie01012025
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17 views2 pages

Pair of Linear Equations

The document contains a series of mathematical problems related to linear equations in two variables, including solving pairs of equations, determining fixed and variable costs, graphing equations, and analyzing the relationship between lines. It also includes word problems involving two-digit numbers and the dimensions of a rectangle. Each problem varies in complexity and requires different methods for solution.

Uploaded by

suzie01012025
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Linear Equations in Two Variables

1. Solve the following pair of linear equations: [2]


y -4x= 1
6x- 5y= 9
2. A part of monthly Hostel charge is fixed and the remaining depends on the number of days
one has taken food in the mess. When Swati takes food for 20 days, she has to pay 13000 as
hostel charges whereas, Mansi who takes food for 25 days pays 3500 as hostel charges. Find
the fixed charges and the cost of food per day. [3]
3. Draw the graphs of the pair of equations: x + 2y = 5 and 2x - 3y = – 4. Also find the points
where the lines meet the x-axis. [4]
4. Find whether the lines representing the following pair of linear equations intersect at a
point, are parallel or coincident: 2x – 3y + 6 = 0, 4x – 5y + 2 = 0 [2]
5. Given a linear equation 3x-5y = 11. Form another linear equation in these variables such that
the geometric representation of the pair so formed is:
(i) intersecting lines
(ii) coincident lines
(iii) parallel lines [3]
6. Solve for x and y
x + 2y – 3= 0
3x – 2y + 7 = 0 [3]
7. Solve for x and y:

[3]

8. Solve for x and y:

6(ax + by) = 3a + 2b
6(bx – ay) = 3b -2a
[3]

9. Solve the following pair of equations by reducing them to a pair of


linear equations:

1 4 1 3
− =2 and + =9 [3]
x y x y

10. Determine graphically whether the following pair of linear equations 2x – 3y = 5;


3x + 4y = – 1 has
(i) a unique solution
(ii) infinitely many solutions or
(iii) no solution [3]
11. In a two-digit number, the digit in the unit place is twice of the digit in the tenth place. If the
digits are reversed, the new number is 27 more than the given number. Find the number.
[4]
12. The area of a rectangle reduces by 160 m if its length is increased by 5 m and breadth is
reduced by 4 m. However, if length is decreased by 10 m and breadth is increased by 2 m,
then its area is decreased by 100 m2. Find the dimensions of the rectangle. [3]
13. Determine the value of m and n so that the following pair of linear equations have infinite
number of solutions.
(2m – l) x + 3y = 5;
3x + (n- l) y = 2 [3]

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