Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

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

Correct Answer:




D) infinite solutions

Description for Correct answer:
Given equations of system

3x + y = 4 ...(i)

6x + 2y = 8 ...(ii)

Here, \( \Large a_{1}=3, b_{1}=1, c_{1}=4, \)

\( \Large a_{2}=6, b_{2}=2, c_{2}=8 \)

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

So, the system of equations has infinite solutions, because it represents a parallel line.

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

Comments

Similar Questions

1). 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

2). 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). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \)

3). 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). \( \Large \frac{1}{5} \)

4). 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

5). 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

6). 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

7). 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

8). A does 20% less work than B. If A can complete a piece of work in \(7\frac{1}{2}\)h, then B can do it in

A). 4 h

B). 6 h

C). 8 h

D). 10 h

9). A takes twice as much time as B and C takes thrice as much time as B to finish a work. Working together, they can finish the work , in 12 days. Find the number of days needed for A to do the work alone.

A). 20

B). 22

C). 33

D). 44

10). A is thrice as good a workman as B and therefore is able to finish a job in 30 days less than B. How many days will they take to finish the job working together?

A). \( \Large 10\frac{1}{4} \)

B). \( \Large 11\frac{3}{4} \)

C). \( \Large 11\frac{1}{4} \)

D). \( \Large 11 \frac{1}{3} \)