Use of cramer`s rule in word problem

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2. BY:ASSOCIATE PROFESSOR NADEE UDDIN
Cramer’s Rule:
It is a method of finding a solution of a system of linear equations.
Consider two linear equations in two variable, x and y.
a1x + b1y = c1 ----------------------(i)
a2x + b2y = c2 ----------------------(ii)
The three determinants involved in finding the value of ‘x’ and ‘y’ are
1 1
2 2
D =
a b
a b
1 1
X
2 2
D =
c b
c b
1 1
y
2 2
D =
a c
a c
Then
yx
x =
DD
and y =
D D

3. Example-12:
Solve the following simultaneous equations by Cramer’s Rule.
x + 2y = 6
2x + 7y = 3
Solution:
D =
1 2
=7 - 4 = 3
2 7
x
6 2
D = 42 - 6 = 36
3 7
=
y
1 6
D = 3 - 12 = -9
2 3
=
By cramer’s rule
D 36xx 12
D 3
D
9y
y 3
D 3
= = =
−
= = = −
Solution set is {(12,-3)}

4. Example-13:
The entry fee at Expo center is Rs.20 for children and Rs.50 for adults.On a
Sunday 2000 people attended the fair and Rs. 85000 is collected. How many
children and how many adults attended the fair at Expo center.
Solution:
Let x be the number of children
and y be the number of adults
X + Y = 2000
20 X + 50 Y = 85000
By cramer’s rule
D = [
1 1
20 50
] = (50)(1) – (20)(1) = 50 – 20 = 30
Dx = [
2000 1
85000 50
] = (2000)(50) – (85000)(1)
= 100000 – 85000 = 15000
Dy = [
1 2000
20 85000
] = (85000)(1) – (2000)(20)
= 85000 – 40000 = 45000
X =
Dx
𝐷
=
15000
30
= 500 (children)
Y =
Dy
𝐷
=
45000
30
= 1500 (Adults)