Answer two questions about Systems A and B: A: x−4y=1
5x+6y=−5
B: x=1+4y
5x+6y=−5
How can we get System B from System A?
A: Replace one equation with itself where a quantity is added to only one side
B: Replace one equation with itself where the same quantity is added to both sides
C: Swap only the right-hand sides of both equations
D: Swap the order of the equations

Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
A: Yes
B: No

Replace one equation with itself where the same quantity is added to both sides

Yes

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

45 degres

step-by-step explanation:

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