Given the system of linear equations. 3x=3y-3 y=x+1 part a: using the method of your choice (graphing, substitution or addition), find the solution to the system of linear equations. include all of your work in your final answer. part b: in two or more complete sentences, explain why you chose the specific method you used to find the solution to the system.

PART A

Convert both of them into Standard Form.

3x = 3y - 3
Subtract 3y from both sides.
3x - 3y = -3

y = x + 1
Subtract x from both sides.
-x + y = 1
Multiply everything by -1 to make x positive.
x - y = -1

3x - 3y = -3
x - y = -1

Multiply x - y = -1 by -3 to make -y the opposite of -3y in 3x - 3y = -3.

3x - 3y = -3
-3x + 3y = 3

Add the equations together.

3x - 3y = -3
-3x + 3y = 3
equals
0 = 0

There are infinitely many solutions.

PART B

First of all, I didn't use graphing because I'm more used to graphing in the y intercept form instead of the x intercept form. I also didn't use substitution because it would take longer than addition, the method I used. Another reason I used addition is because I could easily multiply the -y by -3 to cancel out the -3 in the other equation. When I did this, I realized not only did the y variable cancel out, but so did the x variable and the solution, making it the most efficient way to get the answer.

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