Question

[6.02] and [6.03] Part 1:
Solve the following system of equations. Please show your work to receive full credit.
x - y = 16
2x + y = 2

Part 2:
Explain which method you chose to solve the system and why you felt it was the best choice.

Answer 1

x-y=16
2x+y=2
y=-2x+2
x-(-2x+2)=16
x+2x-2=16
3x=18
x=6
y=-10

i used substitution because it was easy to isolate the y variable.

Answer 2

1. x - y = 16 ----> x = y + 16
2x + y = 2

Now substitute y + 16 in for x in the 2nd equation...
2(y + 16) + y = 2 ( multiply through the parenthesis)
2y + 32 + y = 2 (combine like terms)
3y + 32 = 2 (subtract 32 from both sides to get 3y by itself)
3y + 32 - 32 = 2 - 32
3y = 2 - 32
3y = - 30 (divide by 3 to get y by itself)
3y/3 = - 30/3
y = - 10

Now substitute - 10 in for y in 1st equation to find x
x - y = 16
x - (- 10) = 16
x + 10 = 16 (subtract 10 from each side to get x by itself)
x + 10 - 10 = 16 - 10
x = 16 - 10
x = 6

Now we can check our answers...y = - 10 and x = 6
x - y = 16
10 - (-6) = 16
10 + 6 = 16
16 = 16 (correct)

You can also check it with the other equation...
2x + y = 2
2(6) + (- 10) = 2
12 - 10 = 2
2 = 2 (correct)

ANSWER : x = 6 and y = - 10

2. Substitution is easier to use then addition/elimination when there is only two equations.