• 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

 C) Only I and III

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.

##### 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). $$\Large \frac{15}{4}$$
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
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
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
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). $$\Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq}$$
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). $$\Large \frac{1}{5}$$
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
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?