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th
SGOI Precis_10 _Maths_Linear Equations in Two Variables
1. 2.
For
what
3 x y
of
1, 2k 1 x k 1 y
k
will
2k 1
the
following
pair
of
linear
equations
has
no
solution?
Using the substitution method and elimination method, solve the following system of linear equations. 3 2
3.
value
x
5 2
y 2,
Using ax by
the
x 3
y 2
13 6
.
method
of
cross-multiplication,
solve
the
system
of
linear
equations.
a b, bx ay a b
4.
Find the values of a and b for which the following system of linear equations represents coincident lines, 2 x a 4 y 2b 1, 4 x a 1 y 5b 1 .
5.
Solve the following system of linear equations
2
x
2 3y
1 3 2 , 6 x y
0, x 0, y 0 and
hence find the value
of m for which y mx 4 . 6.
Solve the following system of linear equation graphically. 4 x y 8, 3x 2 y 17 .
7.
The area of a rectangle gets reduced by 9 sq. units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length length by 3 units and breadth by 2 units, the area increased increased by 67 sq. units. Find the dimensions of rectangle.
8.
Solve the following system of linear equations.
9.
The age of father is 3 years more than 3 times the son’s age. 3 years hence the age of the father will be 10years more than twice the age of the son. Find their present ages. A two – digit – digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
10.
7 x 2 y
xy
2
3
5,
8x 7 y
xy
4
9
15, x 0, y 0.
11.
Solve the following system of linear equation
12.
A Two digit number is such that the ten’s digit exceeds twice the unit’s digit by 2 and the number obtained by interchanging the digits is 5 more than three times the sum of the digits. Find the twodigit number. For which values a and b does the following pair of linear equations have infinite number of solutions.
13.
2 x 3 y
x
y
2,
x
y
1
7,
a b x a b y 3a b 2 3 x 4 y 12 0
14.
Find the values of p and q for which
15.
For what value of k will the following f ollowing equations are inconsistent? inconsistent? 2 x 3 y 4, k 2 x by 3k 2 .
16.
A number consists of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
17.
Solve:
18.
Riya travels 300 km to her home partly by train and partly by bus. She takes 4 hrs if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of train and bus separately.
