**Sample Essay**

*Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong.*

*1. What is a system of equations? *

A system of equations can be defined as a group of linear equation containing the same variable and can be solved simultaneously (Purple Math, 2010).

*2. Solve for X and Y in the following problems. Make sure you show all your work so you can get partial credit even if your final answer is wrong.*

*a. X + Y= 10 , 3X + Y = 12 *

Multiplying the first equation by 3 , we get 3X+3Y = 30. Subtracting the second equation from this we get,

3X + 3Y = 30

(-) 3X + (-) Y = (-)12

0X + 2Y = 18

Which gives us

Y = 9.

Putting this value in the first equation we get

X + Y = 10

X + 9 = 10

X = 10 – 9

X = 1

* *

*b. 2X + 5Y = 19 , 3X + 3Y = 15 *

Multiplying the first equation by 3 and second equation by 2 and then subtraction the second one from first we get

6X + 15 Y = 57

(-) 6X + (-) 6Y = (-) 30

0X + 9Y = 27

Which gives us

Y = 3

Putting this value in the second equation and solve

3X + 3Y = 15

3X + 3(3) = 15

3X + 9 = 15

3X = 15 – 9

3X = 6

Which gives us

X = 2

*c. 4X + Y = 22 , 2X + 3Y = 16 *

Multiplying the second equation by 2 and subtracting the first one from the second one

4X+ 6Y = 32

(-)4X + (-)Y = (-) 22

0X + 5Y = 10

Which gives us

Y = 2

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