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
Answers
Step-by-step explanation:
The Condition for no solution = a1/a2 = b1/b2 ≠ c1/c2 (parallel lines)
(i) Yes.
Given pair of equations are
2x+4y - 3 = 0 and 6x + 12y - 6 = 0
Comparing the equations with ax+ by +c = 0;
We get,
a1 = 2, b1 = 4, c1 = - 3;
a2 = 6, b2 = 12, c2 = - 6;
a1 /a2 = 2/6 = 1/3b1 /b2 = 4/12 = 1/3
c1 /c2 = - 3/ - 6 = ½
Here, a1/a2 = b1/b2 ≠ c1/c2, i.e parallel lines
Hence, the given pair of linear equations has no solution.
(ii) No.
Given pair of equations,
x = 2y or x - 2y = 0
y = 2x or 2x - y = 0;
Comparing the equations with ax+ by +c = 0;
We get,
a1 = 1, b1 = - 2, c1 = 0;
a2 = 2, b2 = - 1, c2 = 0;
a1 /a2 = ½
b1 /b2 = -2/-1 = 2
Here, a1/a2 ≠ b1/b2.
Hence, the given pair of linear equations has unique solution.
(iii) No.
Given pair of equations,
3x + y - 3 = 0
2x + 2/3 y = 2
Comparing the equations with ax+ by +c = 0;
We get,
a1 = 3, b1 = 1, c1 = - 3;
a2 = 2, b2 = 2/3, c2 = - 2;
a1 /a2 = 2/6 = 3/2
b1 /b2 = 4/12 = 3/2
c1 /c2 = - 3/-2 = 3/2
Here, a1/a2 = b1/b2 = c1/c2, i.e coincident lines
lean more1. If cos A = 4/5 , then the value of tan A is
(A) 3/5 (B) ¾ (C) 4/3 (D) 5/3
brainly.in/question/26614602
2. If sin A = ½ , then the value of cot A is
(A) √3 (B) 1/√3 (C) √3/2 (D) 1 brainly.in/question/26614602
3. The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is
(A) – 1 (B) 0 (C) 1 (D) 3 2
brainly.in/question/26614755
2. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(A) a unique solution (B) exactly two solutions
(C) infinitely many solutions (D) no solution
brainly.in/question/26617795
Answer:
2 is the answer
Step-by-step explanation: