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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