### The questions given below are basics of Algebra, so it is mandatory for all the students to solve and answers should be submitted in the “comments section”.

**Linear Equations**

1. Solve for x and y: 1.2x + y = 88 and x + 1.2y = 88

2. Solve for x and y: 4x – 6y = 10 and 9y – 6x = 15

3. If 3x + 5y = 12 and kx – 3y = 12 have no simultaneous solution, find the value of k.

4. If 3x + 5y = 12 and kx – 3y = n have infinite simultaneous solutions, then find the value of k × n.

5. If 2x – y + 3z = 15 and 3x + 2y – 6z = 29, find the value of x.

6. If 4 apples, 6 mangoes and 8 oranges costs Rs. 72 and 6 apples, 9 mangoes and 11 oranges cost Rs. 105, find the cost of 1 orange.

7. Find the value of x, y and z that satisfy each of the following three equations:

x + y + z = 1; 2x + y – 2z = 1; and 3x + y + 2z = 1.

8. 5x – y + 2z = 10 and 3x – y + z = 5, find the value of x + y + z.

9. Find the number of natural number solutions to 4x + 5y = 150

10. Find the number of whole number solutions to 8x + 5y = 160.

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