Pair of Linear Equations in Two Variables

1. A.
   consistent
2. B.
   inconsistent
3. C.
   consistent with one solution
4. D.
   consistent with many solutions

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1. A.
   $\dfrac{1}{2}$
2. B.
   $3$
3. C.
   $4$
4. D.
   Not exist

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1. A.
   a unique solution
2. B.
   two solutions
3. C.
   no solution
4. D.
   an infinite number of solutions

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1. A.
   $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$
2. B.
   $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$
3. C.
   $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$
4. D.
   $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$

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1. A.
   $\dfrac{3}{4}$
2. B.
   $\dfrac{4}{3}$
3. C.
   $\dfrac{1}{3}$
4. D.
   $3$

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1. A.
   $y = 3x - 7$
2. B.
   $2x = 9 - 6y$
3. C.
   $x - 3y = 7$
4. D.
   $x = \dfrac{7}{2} - 3y$

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1. A.
   $5x - 4y = 3$
2. B.
   $5x - 4y + 6 = 0$
3. C.
   $15x - 12y - 3 = 0$
4. D.
   $5x - 4y - 6 = 0$

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false, but Reason (R) is true.

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1. A.
   No solution
2. B.
   Unique solution
3. C.
   Two solutions
4. D.
   Infinite solutions

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1. A.
   $a = 2b$
2. B.
   $2a = b$
3. C.
   $a + 2b = 0$
4. D.
   $2a + b = 0$

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1. A.
   $6$
2. B.
   $\dfrac{1}{6}$
3. C.
   $\dfrac{1}{2}$
4. D.
   $\dfrac{1}{3}$

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1. A.
   $x = 5$
2. B.
   $x = -5$
3. C.
   $y = 5$
4. D.
   $y = -5$

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1. A.
   $-6$ only
2. B.
   $6$ only
3. C.
   $\pm 6$
4. D.
   Any real number except $\pm 6$

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1. A.
   coincident
2. B.
   parallel
3. C.
   intersecting at one point
4. D.
   intersecting at right angles

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1. A.
   No solution
2. B.
   $\left(-a, \dfrac{b}{2}\right)$ as its solution
3. C.
   $\left(\dfrac{b}{2}, -a\right)$ as its solution
4. D.
   Infinite solutions

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1. A.
   parallel to x-axis
2. B.
   parallel to y-axis
3. C.
   passing through the origin
4. D.
   passing through the point $(3, 2)$

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1. A.
   $x = 3$
2. B.
   $x = -3$
3. C.
   $y = -3$
4. D.
   $y = 3$

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1. A.
   unique solution
2. B.
   two solutions
3. C.
   no solution
4. D.
   infinite number of solutions

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false, but Reason (R) is true.

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1. A.
   $-2$
2. B.
   $2$
3. C.
   $\dfrac{1}{2}$
4. D.
   $-\dfrac{1}{2}$

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1. A.
   unique solution
2. B.
   exactly two solutions
3. C.
   infinitely many solutions
4. D.
   no solution

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1. A.
   $a^2 - b^2$
2. B.
   $a + b$
3. C.
   $a - b$
4. D.
   $a^2 + b^2$

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1. A.
   exactly one solution
2. B.
   two solutions
3. C.
   infinitely many solutions
4. D.
   no solution

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1. A.
   Parallel
2. B.
   Intersecting
3. C.
   Coincident
4. D.
   Perpendicular to each other

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1. A.
   always intersecting
2. B.
   parallel
3. C.
   always coincident
4. D.
   intersecting or coincident

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1. A.
   $-15x - 9y = 5$
2. B.
   $15x + 9y = 5$
3. C.
   $9x - 15y = 6$
4. D.
   $-15x + 9y = 5$

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1. A.
   consistent with unique solution.
2. B.
   consistent with infinitely many solutions.
3. C.
   inconsistent.
4. D.
   inconsistent but can be made consistent by extending these lines.

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1. A.
   $a = b$
2. B.
   $3a = 2b$
3. C.
   $2a = 3b$
4. D.
   $ab = 6$

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1. A.
   is $k = 3$
2. B.
   does not exist
3. C.
   is $k = -3$
4. D.
   is $k = 4$

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1. A.
   $-10$
2. B.
   $8$
3. C.
   $10$
4. D.
   $-8$

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1. A.
   $(0, -3)$
2. B.
   $(0, 3)$
3. C.
   $(2, 0)$
4. D.
   $(-2, 0)$

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1. A.
   $-\dfrac{1}{2}$
2. B.
   $\dfrac{1}{2}$
3. C.
   $-2$
4. D.
   $2$

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1. A.
   intersecting
2. B.
   parallel
3. C.
   coincident
4. D.
   either intersecting or parallel

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1. A.
   parallel
2. B.
   intersecting at $(b, a)$
3. C.
   coincident
4. D.
   intersecting at $(a, b)$

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1. A.
   $(0, -3)$
2. B.
   $(0, 3)$
3. C.
   $(2, 0)$
4. D.
   $(-2, 0)$

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1. A.
   $3x + y = 900,\; 3x + 5y = 2100$
2. B.
   $x + 3y = 900,\; 3x + 5y = 2100$
3. C.
   $3x + y = 900,\; 5x + 3y = 2100$
4. D.
   $x + 3y = 900,\; 5x + 3y = 2100$

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1. A.
   $x = b, y = a$
2. B.
   $x = -a, y = b$
3. C.
   $x = a, y = b$
4. D.
   $x = a, y = -b$

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1. A.
   $\left(0, \dfrac{-5}{4}\right)$
2. B.
   $\left(0, \dfrac{5}{2}\right)$
3. C.
   $\left(\dfrac{-5}{4}, 0\right)$
4. D.
   $\left(\dfrac{-5}{2}, 0\right)$

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1. A.
   $am \neq bl$
2. B.
   $al \neq bm$
3. C.
   $al = bm$
4. D.
   $am = bl$

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