Verified answer

You can't run the equations together like tnat !

repost with clear identification of the system of equations.

You have a return key on your keypad !

@ß

First get all equations in the slope intercept form of Y = mX + b Then the slopes determine wether the lines are parallel or perpendicular. If the slopes (m) are the same, the lines are parallel. If the slopes are the negative reciprocal of each other then the lines are perpendicular to each other. If neither parallel or perpendicular then the lines are skewed to each other.

1. y - 5 = -2x becomes y = - 2x + 5

2. y = 3x -4

3. y = 2/3 x

4 6y = x = 18 becomes y = x/6 + 3

5. y = -2x + 3 (IS PARALLEL WITH # 1)

6. y = -3x + 2

7. 2y = -3x + 8 becomes y = -3/2 x + 4 (IS PERPENDICULAR WITH #3)

8. y = -6x -4

These are the only onesI see.

1) y -5 = -2x and y + 2x = 3

Step 1) Get y by itself in both equations.

a1) y - 5 = -2x ---- There is a negative 5 on the same side as y so add 5 to both sides.

a2) y = -2x + 5

b1) y + 2x = 3 ---- There is a 2x on the same side as y so subtract 2x from both sides.

b2) y = -2x + 3

The only number you need to look at to figure out if the lines are parallel or perpendicular is the number to the left of x (the coefficient). We can see that both of them are -2 so the slope is the same. When both slopes are the same the answer is always parallel. When the numbers are opposite in all ways ( -2x and 1/2x or 1/3x and -3x) then it is always perpendicular.

So following the same method you should be able to figure out the rest.

1. Parallel

2. Not Parallel

3. Perpendicular

4. Not Parallel

Question 2 is not parallel or perpendicular because while the slopes are the same number, one is positive while the other is negative. (one being -3 and the other +3)

Question 3 is not parallel but is perpendicular to get y by itself both sides must be divided by 2. (slopes turn out to be 2/3 and -3/2 - reciprocals mean perpendicular)

Question 4 is not parallel or perpendicular after both sides is divided by 6 to get y by itself. (slopes turn out to be -1/6x and -6x - both are negative so they are not perpendicular and the number is different so they are not parallel either )

Remember EXACTLY the same is parallel

EXACTLY the opposite is perpendicular.

1. find the slopes of the equations. y = mx + b form has slope = m. Or you can do Ax + By + C = 0 ---> By = -Ax - C ---> y = -A/B - C/B so m = -A/B

2. See if the slopes of the lines are equal or multiply to be -1 (aka they are negative reciprocals...2 and -1/2 for example)

3. If negative reciprocals, they are perpendicular.

4. If the slopes are the same, plug a number in for x to both equations or see if you can reduce one of the equations to get the other. If x into both equations gives you the same number, they are the same line. If one reduces to the other, ie 2y = 2x + 2 and y = x + 1, divide the first equation by 2 and you get the second equation, then they are the same line. If they have the same slope but do not share a point they are parallel.