40. The graph of the following system yields perpendicular lines.

x + 2y = -10
-4y = 2x + 20

(True?)

47. The graph of the following system yields parallel lines.

2y = -10 + x
-4y = 2x + 20

(True)

48. The graph of the following system yields parallel lines.

x - 2y = 1
y = -3x + 10

(False)

Are these correct?

Thanks
-MC

47.

2y = -10 + x ----> y = (1/2)x - 5
-4y = 2x + 20 ---> y = (-1/2)x - 5
one slope is 1/2 then other is -1/2, so NOT parallel

your best way is to rewrite in the form
y = mx + b like I did above.

Why are you unsure about the first one ?

Thanks; are the other 2 correct?

-MC

To determine whether the graphs of the given systems of equations yield perpendicular or parallel lines, you can examine the slopes of the lines.

For perpendicular lines, the slopes of the two lines must be negative reciprocals of each other. This means that if one line has slope m, the other line must have slope -1/m.

For parallel lines, the slopes of the two lines must be equal. This means that if one line has slope m, the other line must also have slope m.

Now let's analyze each system of equations:

40.
x + 2y = -10
-4y = 2x + 20

To find the slopes of the lines from these equations, we need to rewrite them in the form y = mx + b, where m is the slope.

From the first equation, rearrange it to y = (-1/2)x - 5.
The slope of this line is -1/2.

From the second equation, rearrange it to y = (-1/2)x - 5.
The slope of this line is also -1/2.

Since the slopes of both lines are the same, they are parallel, not perpendicular.
So, the statement "The graph of the following system yields perpendicular lines" is false.

47.
2y = -10 + x
-4y = 2x + 20

Rearranging the first equation to y = (1/2)x - 5 and the second equation to y = (-1/2)x - 5, we find that the slopes of both lines are 1/2.
Since the slopes are the same, the lines are parallel.
So, the statement "The graph of the following system yields parallel lines" is true.

48.
x - 2y = 1
y = -3x + 10

From the first equation, rearrange it to y = (1/2)x - 1/2.
The slope of this line is 1/2.

From the second equation, the slope is -3.

Since the slopes of the two lines are not the same, they are not parallel.
So, the statement "The graph of the following system yields parallel lines" is false.

To summarize:
40. The statement "The graph of the following system yields perpendicular lines" is false.
47. The statement "The graph of the following system yields parallel lines" is true.
48. The statement "The graph of the following system yields parallel lines" is false.