Question

Can someone help me with the system of equations: 4x + 2y = 10 and 3y = -6x + 25?

a) They are perpendicular lines.
b) They are parallel lines.
c) They are neither perpendicular nor parallel.

Answer 1

The given system of equations is parallel lines.

Step-by-step explanation:

The given system of equations is:

4x + 2y = 10

3y = -6x + 25

To determine whether these equations are parallel, perpendicular, or neither, we need to compare their slopes. In the first equation, the coefficient of x is 4, and the coefficient of y is 2. So, the slope of the first equation is -2.

In the second equation, the coefficient of x is -6, and the coefficient of y is 3. So, the slope of the second equation is -6/3 = -2.

Since the slopes of both equations are the same (-2), the lines represented by these equations are parallel.

Therefore, the answer is b) They are parallel lines.