Topics

The graphs of ax + by = c, dx + ey = f will be
I. parallel, if the system has no solution.
II. coincident, if the system has finite numbers of solutions.
III. intersecting, if the system has only one solution.
Which of the above statements are correct?


A) Only I and II

B) Only ll and Ill

C) Only I and III

D) I, II and Ill

Correct Answer:
C) Only I and III

Description for Correct answer:

ax + by = c and dx + ey = f

\( \Large \frac{a_{1}}{a_{2}}=\frac{a}{d}, \frac{b_{1}}{b_{2}}=\frac{b}{e}, \frac{c_{1}}{c_{2}}=\frac{c}{f} \)

Because, \( \Large \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \)

Therefore, \( \Large \frac{b}{e} = \frac{c}{f} \)

It represents a pair of parallel lines.

Because, \( \Large \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \)

Therefore, \( \Large \frac{a}{d} = \frac{b}{e}\)

Therefore, system has unique solution and represents a pair of intersecting lines.


Part of solved Linear Equations questions and answers : >> Aptitude >> Linear Equations




Comments
No comments available




Similar Questions
1). If \( \Large 3^{x+y}=81 \) and \( \Large 81^{x-y}=3 \), then what is the value of x?
A). \( \Large \frac{17}{16} \)
B). \( \Large \frac{17}{8} \)
C). \( \Large \frac{17}{4} \)
D). \( \Large \frac{15}{4} \)
-- View Answer
2). Ten chairs and six tables together cost Rs.6200, three chairs and two tables together cost Rs.1900. The cost of 4 chairs and 5 tables is
A). Rs.3000
B). Rs.3300
C). Rs.3500
D). Rs.3800
-- View Answer
3). The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has
A). a unique solution x = 1, y=1
B). a unique solution x = 0, y = 4
C). no solution
D). infinite solutions
-- View Answer
4). If x+ y - 7 = 0 and 3x + y -13 = 0, then what is \( \Large 4x^{2} + y^{2} + 4xy\) equal to?
A). 75
B). 85
C). 91
D). 100
-- View Answer
5). The solution of the equations \( \Large \frac{p}{x}+\frac{q}{y} \  and  \  \frac{q}{x}+\frac{p}{y} \) n is
A). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)
B). \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)
C). \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \)
D). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)
-- View Answer


6). If \( \Large \frac{3}{x+y}+\frac{2}{x-y}=2 \) and \( \Large \frac{9}{x+y}-\frac{4}{x-y}=1 \), then what is the value of \( \Large \frac{x}{y} \)?
A). \( \Large \frac{3}{2} \)
B). 5
C). \( \Large \frac{2}{3} \)
D). \( \Large \frac{1}{5} \)
-- View Answer
7). If \( \Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y} \) and \( \Large \frac{a}{b}+\frac{b}{a}= x - y \) , then what is the value of x?
A). \( \Large \frac{a+b}{a} \)
B). \( \Large \frac{a+b}{b} \)
C). \( \Large \frac{a-b}{a} \)
D). None of these
-- View Answer
8). If \( \Large \frac{x}{2}+\frac{y}{3}=4 \) and \( \Large \frac{2}{x}+\frac{3}{y}=1 \) then what is x + y equal to?
A). 11
B). 10
C). 9
D). 8
-- View Answer
9). A mason can build a tank in 12 h. After working for 6 h, he took the help of a boy and finished the work in another 5 h. The time that the boy will take alone to complete the work is
A). 30 h
B). 45 h
C). 60 h
D). 64 h
-- View Answer
10). A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work ?
A). 36
B). 12
C). 18
D). 9
-- View Answer
Home About Us Terms and Conditions Privacy Policy Contact us