Chapter 3 Pair of Linear Equation in Two Variables NCERT Exemplar Solutions Exercise 3.2 Class 10 Maths
![Chapter 3 Pair of Linear Equation in Two Variables NCERT Exemplar Solutions Exercise 3.2 Class 10 Maths Chapter 3 Pair of Linear Equation in Two Variables NCERT Exemplar Solutions Exercise 3.2 Class 10 Maths](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcl9goOalAFMyMesNxxQQzO5eY6ichN14dWNy6KMrC0Pwqjh_i0jnxPFleE4D7xndo11Gjs95vqA5I3hV0qactt-3U2SNqZqVL9h6RAWvWwviPg1LjRUHXO7YIK0huyBP9OZsshtjJcsIO_r-dTdYoD41OQF7yLSzzrP5qDZ-h74cN_QmRhbzImJ_6_Q/s16000/class-10-maths-exemplar-solution-for-chapter-3-pair-of-linear-equations-in-two-variables-exercise-3-2.jpg)
Chapter Name | NCERT Maths Exemplar Solutions for Chapter 3 Pair of Linear Equation in Two Variables Exercise 3.2 |
Book Name | NCERT Exemplar for Class 10 Maths |
Other Exercises |
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Related Study | NCERT Solutions for Class 10 Maths |
Exercise 3.2 Solutions
1. Do the following pair of linear equations have no solution? Justify your answer.
(i) 2x + 4y = 3
12y + 6x = 6
(ii) x = 2y
y = 2x
(iii) 3x + y – 3 = 0
2x + 2/3y = 2
Solution
(i) Yes
According to question,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhh7xXz-2DVNVvRz8HApTK2RWnEXXjnIiXHlStLF9dct3CNlwAFgCPujKz_AcAOR34PUbhLOcw-CRDQYjY2-sMhjeQJRzY7u_JxWtUHkBZP23U23fL7e_MUjmYeTKa3SbG77FHs-qIw9pJk6eXixWNtWatPKb4_qWdKdJab5IZlf8RhEIg0rFQCLT1c/w117-h289/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%201.JPG)
Hence, the pair of linear equations has no solutions.
(ii) No,
According to question,
Hence the pair of linear equations have unique solutions.
(iii) No
According to question,
a1 = 3,
b1 = 1,
a1 = 3,
b1 = 1,
c1 = – 3,
a2 = 2,
b2 = 2/3,
c2 = – 2,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIZhPhtOd_vj5JRzeizKMAZHavQAOO1GcQZPIdO34FUG8p0tcghv-5rdFa6eb2a_GnRSbcxr1G2hchtKN4snPOmOhfLFjM6_jBZ6RLG467ddqLpc3KTFdh3mImb4XjQ7yRtnzRRvcdgqebAvE5PuD9PA8sQxK8QDFmwWBtOGpeApO7FtMnAvNSJWfa/w108-h229/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%203.JPG)
So, the pair of linear equations are coincident.
So, the pair of linear equations are coincident.
2. Do the following equations represent a pair of coincident lines? Justify your answer.
(i) 3x + 1/7y = 3
7x + 3y = 7
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge5Oi0rC2O8b81SJaHsc90EMhNEtTGaysdD3RqiVVPORU_1m6QpyxmIFQVRVZk5HZUYMeoE1CT3sGqy5ll_N6zeGWxzc81Mbz2Sm_Ot7ReJgKQeAnNJQHh6oZKFue1AYYeSNAnFHJoLBQZJwzj0VAIW0ynRAMDB-lG3k1rl_RXtaCOhsb8IqXmHaY1/w108-h53/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%204.JPG)
(ii) –2x – 3y = 1
6y + 4x = – 2
(iii) x/2 + y + 2/5 = 0
4x + 8y + 5/16 = 0
Solution
For coincident lines,
(i) No
Given pair of linear equations are:
3x + 1/7y = 3
7x + 3y = 7
We have
a1 = 3,
b1 = 1/7,
b1 = 1/7,
c1 = – 3,
and
and
a2 = 7,
b2 = 3,
c2 = – 7,
The given pair of linear equations has unique solution.
(ii) Yes,
The pair of linear equations are,
– 2x – 3y – 1 = 0 and 4x + 6y + 2 = 0;
We have
a1 = -2,
b1 = -3,
b1 = -3,
c1 = -1,
And
And
a2 = 4,
b2 = 6,
c2 = 2,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLj3nlzWAWxCgL24L4u3S1IJt6AUGJE2u2VQLwxElkc1NJgS557m7U8QVK5Z8SlN3JGW3BN0iXX7UdWyAhovp8Rk4COTlL6CJWZ3E0sgz-jwMMuHPPaAEPXrbtn1ANskVRpmpLx5lsWwrh2RWBzYH5Y2roUM8qwrJ5U4jRgPqLNIlr90MAwWHAEHjl/w130-h248/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%206.JPG)
The given pair of linear equations is coincident.
The given pair of linear equations is coincident.
(iii) No,
Pair of linear equations are:
x/2 + y + 2/5 = 0
4x + 8y + 5/16 = 0
We have,
a1 = 1/2,
b1 = 1,
b1 = 1,
c1 = 2/5,
And
And
a2 = 4,
b2 = 8,
c2 = 5/16,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheGvplbvsgDdfmbrxRac19fLkj8zVsIj0-UtkuEQMnYspi4XMPUBLFXZG9dIMbkXhdh7O9ErIOtmVTETztjjhJczeVPKQhYbw72oVpyqcK-9fONUIKtlVu9k5OhmlLfnPmNoko2sLwB4GNrYgAArf-sRBRrofOxC1S1K0a9lbFPvl5OFlHYjRXNTrM/w107-h228/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%207.JPG)
Hence, the given pair of linear equations has no solution.
3. Are the following pair of linear equations consistent? Justify your answer.
(i) –3x– 4y = 12
4y + 3x = 12
(ii) (3/5) x – y = 1⁄2
(1/5) x – 3y= 1/6
(1/5) x – 3y= 1/6
(iii) 2ax + by = a
ax + 2by – 2a = 0; a, b ≠ 0
(iv) x + 3y = 11
2 (2x + 6y) = 22
Solution
For pair of linear equations to be consistent:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGZXmT7Qjy82LAqFHmD6LWpI37k2xYCbWokqbvxGjiAs8BcVD5TQe--UYa4BO1h9_egPOKaX-cUml9Nb9wV5o0FiDOo2UBrMi87Uhq5bhCog9lS0-ZCvoLEKR09AvcyDEqbbYQYGEPoTSDSqSqONHYkp2AbdmSj3w5ECbb5m1RTfdMJ2aUT9AKFZ_a/w274-h88/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%208.JPG)
(i) No.
The given pair of linear equations
– 3x – 4y – 12 = 0
4y + 3x – 12 = 0
We get,
a1 = -3,
b1 = -4,
b1 = -4,
c1 = -12,
a2 = 3,
b2 = 4,
c2 = -12,
The pair of linear equations has no solution, i.e., inconsistent.
(ii) Yes.
The given pair of linear equations
(3/5)x – y = 1⁄2
(1/5)x – 3y = 1/6
We have,
a1 = 3/5,
b1 = -1,
b1 = -1,
c1 = -1/2,
a2 = 1/5,
b2 = 3,
c2 = -1/6,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijEV9qg1VFksD9CCB3o0T12BjjI0vGPC1c9g_-hz05QSAtI35RXVPp3qE4PyH5-zhrO6_7dwclhTD3opKqlmwenzcTqOETewC2knxVV8Sx_VL0q1gHqMM9a5fcW1S5MN4Bf3B5xF3uHRYc7DslMzDafcJybhBSOl81geG53uWl5sQkYHbV0JdigPhw/w84-h228/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%2010.JPG)
The given pair of linear equations has unique solution, i.e., consistent.
(iii) Yes.
The given pair of linear equations –
2ax + by –a = 0
4ax + 2by – 2a = 0
We have,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8FXCztrc6nwoCOMU_xMuH1EjpkHA2X3-NDRr_wkSTcCJ55wIOD9uulix2DXrG-6njx-6GVBlCIWMy3hyi61CxNP_adgeOYvQbB7SGeRW6Fj06onrNCzaXXZ9rnTDr0ueNX8B2q0nm-jnkvkI5HJb0wJKuH68FXRyZOcaUS0uAmHgCEHFzlToTYEvG/w103-h213/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%2011.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_c0y0GL8BwQ4qIV60VzS4hlmNJGp_JK1pS9vjVtMD3SQ4pgzuBQGgorHrMED1EHBVjfb6CPLZlrxETMJosPWVB4xANzwgn7yAiWZ7uytt8ROQnHGQMAm7gjGacvAZx3HPJYW1IkIPBFnLQU9Ai6ROFSIQdnZymOmbrpYBeov64BeWSMJN0la88tNY/w103-h258/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%2012.JPG)
The given pair of linear equations has no solution.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigRqJ2GYFh0kjEcpJWxUOMnRnG7o05iTCEeUDUrLdWWwGTmN08iHYbf12cAz5hFAxyyW9BYBgpkEQj_8YfdCM20a1neFi_NDe0zZY_coa1xfbp9u8NVLlYD92pQEgZUeJm2VwpA4RRRDih3Ni4615p3FeuAaeKqEyIsYsnDVhIEdco9u76Rc6cSmr0/w101-h290/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%2014.JPG)
a1 = 2a,
b1 = b,
b1 = b,
c1 = -a,
a2 = 4a,
b2 = 2b,
c2 = -2a,
The given pair of linear equations has infinitely many solution, i.e., consistent
(iv) No.
The given pair of linear equations
x + 3y = 11
2x + 6y = 11
We have,
a1 = 1,
b1 = 3,
b1 = 3,
c1 = 11,
a2 = 2,
b2 = 6,
c2 = 11,
The given pair of linear equations has no solution.
4. For the pair of equations λx + 3y = –7 , 2x + 6y = 14to have infinitely many solutions, the value of λ should be 1. Is the statement true? Give reasons.
Solution
λx + 3y + 7 = 0 .
2x + 6y – 14 = 0
For infinitely many solutions,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPSRg1ehjpKszZ-BgWb9AJuNCcaigLii7JxlZCJMmUTXBEAVcTM5OK0blXQ9249q8rHtpmhXL_m-W9w-afFJPr56KrxPB83E5k6Lm0JTb4ouLxDZ486R66NeK_lZYc3AhGekXeRfoTuZBjPMJtDI4GQmYlfIND29Nq5c6mvy0V3x4tMK3DXIiJd1su/w218-h436/Class%2010%20Chapter%203%20Pair%20of%20Linear%20Equation%20in%20Two%20Variable%20Exercise%20-%203.2%20img%2013.JPG)
So, the given statement is not true.
For infinitely many solutions,
So, the given statement is not true.
5. For all real values of c, the pair of equations x – 2y = 8 5x – 10y = c have a unique solution. Justify whether it is true or false.
Solution
(Not true)
System of linear equations are
x – 2y = 8 ...(i)
5x – 10 = c ...(ii)
Hence, system of linear equations can never have unique solution.
So, the given statement is not true.
6. The line represented by x = 7 is parallel to the x–axis. Justify whether the statement is true or not.
Solution
The line x = 7 is the form of x = a. The graph of the equation is a line parallel to the y–axis.
Hence, the given statement is false.