Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

9x + 5y = 10
3y − 2x = 8

Given: x + 2y = 1
            3x + y = 4

3x + y + z = 2
2x − 4y + 3z = − 1
4x + y − 3z = − 11

x − 4y − z = 11
2x − 5y + 2z = 39
− 3x + 2y + z = 1

6x + y − 3z = 5
x + 3y − 2z = 5
2x + y + 4z = 8

x+ y = 5
y + z = 3
x + z = 4

2y − 3z = 0
x + 3y = − 4
3x + 4y = 3

5x − 7y + z = 11
6x − 8y − z = 15
3x + 2y − 6z = 7

2x − 3y − 4z = 29
− 2x + 5y − z = − 15
3x − y + 5z = − 11

x + y + z + 1 = 0
ax + by + cz + d = 0
a²x + b²y + x²z + d² = 0

3x + y = 5
− 6x − 2y = 9

3x − y + 2z = 3
2x + y + 3z = 5
x − 2y − z = 1

3x − y + 2z = 6
2x − y + z = 2
3x + 6y + 5z = 20.

x − y + z = 3
2x + y − z = 2
− x − 2y + 2z = 1

x + 2y = 5
3x + 6y = 15

x + y − z = 0
x − 2y + z = 0
3x + 6y − 5z = 0

2x + y − 2z = 4
x − 2y + z = − 2
5x − 5y + z = − 2

x − y + 3z = 6
x + 3y − 3z = − 4
5x + 3y + 3z = 10

A salesman has the following record of sales during three months for three items A, B and C which have different rates of commission 

Find out the rates of commission on items A, B and C by using determinant method.

An automobile company uses three types of steel S₁, S₂ and S₃ for producing three types of cars C₁, C₂and C₃. Steel requirements (in tons) for each type of cars are given below : 

Using Cramer's rule, find the number of cars of each type which can be produced using 29, 13 and 16 tons of steel of three types respectively.