Question

What is true about the lines represented by this system of linear equations?

2y = 4x + 12
-4y = -8x + 24
Α. The lines are perpendicular.
B. The lines are parallel.
C. The lines coincide.
D. The lines intersect, but are not perpendicular.

Answer 1

After converting the given system of linear equations to slope-intercept form, it is evident that both lines have the same slope but different y-intercepts, indicating that they are parallel to each other.

Step-by-step explanation:

When analyzing the system of linear equations given:

• 2y = 4x + 12
• -4y = -8x + 24

We must assess the slope and y-intercept. The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope and 'b' the y-intercept. First, we convert the given equations to slope-intercept form:

• y = 2x + 6 (Dividing the first equation by 2)
• y = 2x - 6 (Dividing the second equation by -4)

We can see that both lines have the same slope, 2, but different y-intercepts (6 and -6, respectively). Therefore, these lines are parallel to each other since they have identical slopes and different y-intercepts.

The correct choice is B. The lines are parallel.