Pair of Linear Equations in two variables. 1) Is the system of linear equations 2x + 3y + 9 = 0 and 4x + 6y = 18 consistent.
Justify your answer.
2) Write a linear equation which is dependent to - 2x + 3y = 7.
3) Given a linear equation 2x + 3y = 10, write another linear equation so that the lines
represented by the pair are i) interesting ii) parallel.
4) Find k if the system of equations x + 2y = 5 and 3x + ky + 15 = 0 have
i) a unique solution ii) inconsistent.
5) For what value of ‘’a” the pair of linear equation ax + 3y = a – 3 and
12x + ay = a has no solution.
6) For what value of p and q for which the system of equation represent coincident
lines 2x + 3y = 7 and p(x + y) – q(x-y) = (3p + q – 2).
7) Solve : i) 5
+ - 2
−
= - 1 , 15
+
+
7
−
= 10.
ii) 2
√
+
3
√
= 2 , 4
√
- 9
√
= - 1.
iii) 2
-
2
= 0 , 2
- 2
= a + b.
8) Solve : 99x + 101y = 499
101x + 99y = 501
9) If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces
to 1. It becomes 1
2
if we only add 1 to the denominator, find the fraction?
10) 2 men and 7 boys can do a piece of work in 4 days . It is done by 4 men and 4 boys in
3 days . Find the time taken by one man alone to finish the work and also that
taken by one boy alone.
11) In a two digit number the unit’s digit is twice the ten’s digit. If 27 is added to the
number the digits interchange their places. Find the number.
12) A motor boat can travel 30 km upstream and 28 km downstream in 7 hours.
It can travel 21 km upstream and return in 5 hours. Find the speed of the boat
in still water and the speed of the stream.
13) Draw the graph of 2x + y = 6 and 2x – y + 2 = 0 . Also find the area of the region
bounded by these lines and x axis