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Write a pair of linear equations which h...

Write a pair of linear equations which has the unique solution `x = -1` and `y = 3`. How many such pairs can you write ?

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To write a pair of linear equations that has a unique solution of \( x = -1 \) and \( y = 3 \), we can follow these steps: ### Step 1: Identify the solution point The unique solution given is \( (x, y) = (-1, 3) \). ### Step 2: Formulate the equations We can start by using the point-slope form of a linear equation. The general form of a linear equation is: \[ ax + by + c = 0 \] ...
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(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? 2x + 3y = 7 (a - b)x + (a + b)y = 3a + b - 2 (ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1 (2k - 1)x + (k - 1)y = 2k + 1

Write an equation of a line passing through the point representing solution of the pair of linear equations x+y=2 and 2x-y=1, How many such lines can we find?

For which values of a and b will the following pair of linear equations has infinitely many solutions ? x + 2y = 1 (a-b) x + (a + b ) y = a + b -2

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NCERT EXEMPLAR ENGLISH-PAIR OF LINEAR EQUATIONS IN TWO VARIABLES-Exercise 3.3 Short Answer Type Questions
  1. For which values of a and b will the following pair of linear equation...

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  2. Find the values of p in (i) to (iv) and p and q in (v) for the followi...

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  3. Two straight paths are represented by the equations x - 3y = 2 and -2...

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  4. Write a pair of linear equations which has the unique solution x = -1 ...

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  5. If 2x + y = 23 and 4x - y = 19, then find the values of 5y - 2x and (...

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  6. Find the values of x and y in the following rectangle

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  7. Solve the following pairs of equations (i) x + y = 3.3, " " (0.6)/(...

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  8. Find the solution of the pair of equations (x)/(10) + (y)/(5) - 1 = 0 ...

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  9. By the graphical method, find whether the following pair of equations ...

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  10. Draw the graph of the pair of equations 2x+y=4 and 2x-y=4. Write the v...

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  11. Write an equation of a line passing through the point representing sol...

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  12. If (x+1) is a factor of 2x^(3)+ax^(2)+2bx+1, then find the value of a ...

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  13. If the angles of a triangle are x, y and 40^(@) and the difference bet...

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  14. Two years ago, Salim was thrice as old as his daughter and six years l...

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  15. The age of the father is twice the sum of the ages of his two children...

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  16. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of th...

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  17. There are some students in the two examination halls A and B. To make ...

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  18. A shopkeeper gives books on rent for reading. She takes a fixed charge...

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  19. In a competitive examination, 1 mark is awarded for each correct answ...

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  20. The angles of a cyclic quadrilateral ABCD are angleA=(6x+10)^(@), angl...

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